LMFDB - Embedded newform 930.2.v.a.821.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(401,930)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("930.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.v (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			821.13
Character	$\chi$	$=$	930.821
Dual form			930.2.v.a.401.13

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(-1.10868 + 1.33073i) q^{3} +(-0.309017 + 0.951057i) q^{4} -1.00000i q^{5} +(-1.72824 - 0.114757i) q^{6} +(0.0841834 - 0.259090i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.541668 - 2.95069i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(-1.10868 + 1.33073i) q^{3} +(-0.309017 + 0.951057i) q^{4} -1.00000i q^{5} +(-1.72824 - 0.114757i) q^{6} +(0.0841834 - 0.259090i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.541668 - 2.95069i) q^{9} +(0.809017 - 0.587785i) q^{10} +(0.177677 - 0.546834i) q^{11} +(-0.922996 - 1.46563i) q^{12} +(3.97653 - 5.47323i) q^{13} +(0.259090 - 0.0841834i) q^{14} +(1.33073 + 1.10868i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.82647 - 5.62130i) q^{17} +(2.06878 - 2.17259i) q^{18} +(1.95325 - 1.41912i) q^{19} +(0.951057 + 0.309017i) q^{20} +(0.251445 + 0.399272i) q^{21} +(0.546834 - 0.177677i) q^{22} +(1.63581 + 5.03452i) q^{23} +(0.643198 - 1.60820i) q^{24} -1.00000 q^{25} +6.76528 q^{26} +(4.52710 + 2.55056i) q^{27} +(0.220395 + 0.160126i) q^{28} +(-1.97255 + 1.43314i) q^{29} +(-0.114757 + 1.72824i) q^{30} +(0.919844 - 5.49126i) q^{31} -1.00000i q^{32} +(0.530700 + 0.842702i) q^{33} +(3.47416 - 4.78177i) q^{34} +(-0.259090 - 0.0841834i) q^{35} +(2.97366 + 0.396658i) q^{36} +9.86212i q^{37} +(2.29618 + 0.746074i) q^{38} +(2.87468 + 11.3597i) q^{39} +(0.309017 + 0.951057i) q^{40} +(-4.40895 - 6.06840i) q^{41} +(-0.175222 + 0.438110i) q^{42} +(1.26819 + 1.74551i) q^{43} +(0.465165 + 0.337962i) q^{44} +(-2.95069 + 0.541668i) q^{45} +(-3.11150 + 4.28262i) q^{46} +(7.33436 - 10.0949i) q^{47} +(1.67912 - 0.424916i) q^{48} +(5.60308 + 4.07087i) q^{49} +(-0.587785 - 0.809017i) q^{50} +(9.50539 + 3.80168i) q^{51} +(3.97653 + 5.47323i) q^{52} +(-3.15692 - 9.71600i) q^{53} +(0.597520 + 5.16168i) q^{54} +(-0.546834 - 0.177677i) q^{55} +0.272423i q^{56} +(-0.277064 + 4.17258i) q^{57} +(-2.31887 - 0.753446i) q^{58} +(-7.48784 + 10.3061i) q^{59} +(-1.46563 + 0.922996i) q^{60} -10.5251i q^{61} +(4.98319 - 2.48351i) q^{62} +(-0.810094 - 0.108059i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-5.47323 - 3.97653i) q^{65} +(-0.369823 + 0.924673i) q^{66} +9.75486 q^{67} +5.91059 q^{68} +(-8.51316 - 3.40484i) q^{69} +(-0.0841834 - 0.259090i) q^{70} +(-4.16863 + 1.35447i) q^{71} +(1.42697 + 2.63889i) q^{72} +(11.2674 + 3.66099i) q^{73} +(-7.97862 + 5.79681i) q^{74} +(1.10868 - 1.33073i) q^{75} +(0.746074 + 2.29618i) q^{76} +(-0.126722 - 0.0920686i) q^{77} +(-7.50051 + 9.00274i) q^{78} +(-5.47101 + 1.77764i) q^{79} +(-0.587785 + 0.809017i) q^{80} +(-8.41319 + 3.19659i) q^{81} +(2.31792 - 7.13383i) q^{82} +(7.86138 - 5.71163i) q^{83} +(-0.457431 + 0.115757i) q^{84} +(-5.62130 + 1.82647i) q^{85} +(-0.666726 + 2.05197i) q^{86} +(0.279802 - 4.21381i) q^{87} +0.574975i q^{88} +(-4.69430 + 14.4476i) q^{89} +(-2.17259 - 2.06878i) q^{90} +(-1.08330 - 1.49103i) q^{91} -5.29360 q^{92} +(6.28755 + 7.31209i) q^{93} +12.4780 q^{94} +(-1.41912 - 1.95325i) q^{95} +(1.33073 + 1.10868i) q^{96} +(0.889534 - 2.73770i) q^{97} +6.92579i q^{98} +(-1.70978 - 0.228069i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9}+O(q^{10}) $ 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9	$ 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9} + 20 q^{10} - 10 q^{13} - 20 q^{16} - 12 q^{18} - 12 q^{19} + 30 q^{21} + 10 q^{22} - 80 q^{25} + 18 q^{28} + 16 q^{31} + 72 q^{33} + 10 q^{34} + 8 q^{36} + 54 q^{39} - 20 q^{40} + 50 q^{43} + 8 q^{45} - 10 q^{46} + 8 q^{49} - 44 q^{51} - 10 q^{52} - 10 q^{55} + 30 q^{58} + 28 q^{63} + 20 q^{64} + 66 q^{66} + 60 q^{67} + 20 q^{69} - 12 q^{70} + 12 q^{72} - 20 q^{73} - 18 q^{76} + 8 q^{78} + 40 q^{79} + 16 q^{81} - 4 q^{82} - 60 q^{84} - 72 q^{87} - 12 q^{90} + 10 q^{91} + 104 q^{93} - 12 q^{94} - 178 q^{97}+O(q^{100}) $ 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9 + 20 * q^10 - 10 * q^13 - 20 * q^16 - 12 * q^18 - 12 * q^19 + 30 * q^21 + 10 * q^22 - 80 * q^25 + 18 * q^28 + 16 * q^31 + 72 * q^33 + 10 * q^34 + 8 * q^36 + 54 * q^39 - 20 * q^40 + 50 * q^43 + 8 * q^45 - 10 * q^46 + 8 * q^49 - 44 * q^51 - 10 * q^52 - 10 * q^55 + 30 * q^58 + 28 * q^63 + 20 * q^64 + 66 * q^66 + 60 * q^67 + 20 * q^69 - 12 * q^70 + 12 * q^72 - 20 * q^73 - 18 * q^76 + 8 * q^78 + 40 * q^79 + 16 * q^81 - 4 * q^82 - 60 * q^84 - 72 * q^87 - 12 * q^90 + 10 * q^91 + 104 * q^93 - 12 * q^94 - 178 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	−1.10868	+	1.33073i	−0.640095	+	0.768295i
$3$	−1.10868	+	1.33073i	−0.640095	+	0.768295i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−1.72824	−	0.114757i	−0.705553	−	0.0468495i
$7$	0.0841834	−	0.259090i	0.0318183	−	0.0979267i	−0.933886	−	0.357571i	$-0.883605\pi$
$7$	0.0841834	−	0.259090i	0.0318183	−	0.0979267i	0.965704	+	0.259644i	$0.0836052\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	−0.541668	−	2.95069i	−0.180556	−	0.983565i
$10$	0.809017	−	0.587785i	0.255834	−	0.185874i
$11$	0.177677	−	0.546834i	0.0535717	−	0.164877i	−0.920691	−	0.390292i	$-0.872374\pi$
$11$	0.177677	−	0.546834i	0.0535717	−	0.164877i	0.974263	+	0.225416i	$0.0723740\pi$
$12$	−0.922996	−	1.46563i	−0.266446	−	0.423092i
$13$	3.97653	−	5.47323i	1.10289	−	1.51800i	0.271396	−	0.962468i	$-0.412515\pi$
$13$	3.97653	−	5.47323i	1.10289	−	1.51800i	0.831495	−	0.555532i	$-0.187485\pi$
$14$	0.259090	−	0.0841834i	0.0692447	−	0.0224990i
$15$	1.33073	+	1.10868i	0.343592	+	0.286259i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.82647	−	5.62130i	−0.442985	−	1.36337i	−0.884679	−	0.466201i	$-0.845622\pi$
$17$	−1.82647	−	5.62130i	−0.442985	−	1.36337i	0.441694	−	0.897166i	$-0.354378\pi$
$18$	2.06878	−	2.17259i	0.487616	−	0.512085i
$19$	1.95325	−	1.41912i	0.448106	−	0.325568i	−0.340742	−	0.940157i	$-0.610678\pi$
$19$	1.95325	−	1.41912i	0.448106	−	0.325568i	0.788847	+	0.614589i	$0.210678\pi$
$20$	0.951057	+	0.309017i	0.212663	+	0.0690983i
$21$	0.251445	+	0.399272i	0.0548699	+	0.0871283i
$22$	0.546834	−	0.177677i	0.116585	−	0.0378809i
$23$	1.63581	+	5.03452i	0.341091	+	1.04977i	0.963643	+	0.267192i	$0.0860956\pi$
$23$	1.63581	+	5.03452i	0.341091	+	1.04977i	−0.622553	+	0.782578i	$0.713904\pi$
$24$	0.643198	−	1.60820i	0.131292	−	0.328272i
$25$	−1.00000			−0.200000
$26$	6.76528			1.32678
$27$	4.52710	+	2.55056i	0.871241	+	0.490855i
$28$	0.220395	+	0.160126i	0.0416507	+	0.0302610i
$29$	−1.97255	+	1.43314i	−0.366293	+	0.266127i	−0.755672	−	0.654950i	$-0.772690\pi$
$29$	−1.97255	+	1.43314i	−0.366293	+	0.266127i	0.389379	+	0.921078i	$0.372690\pi$
$30$	−0.114757	+	1.72824i	−0.0209517	+	0.315533i
$31$	0.919844	−	5.49126i	0.165209	−	0.986259i
$31$	0.919844	−	5.49126i	0.165209	−	0.986259i
$32$		−	1.00000i		−	0.176777i
$33$	0.530700	+	0.842702i	0.0923830	+	0.146696i
$34$	3.47416	−	4.78177i	0.595813	−	0.820066i
$35$	−0.259090	−	0.0841834i	−0.0437942	−	0.0142296i
$36$	2.97366	+	0.396658i	0.495610	+	0.0661097i
$37$			9.86212i			1.62132i	0.585515	+	0.810661i	$0.300892\pi$
$37$			9.86212i			1.62132i	−0.585515	+	0.810661i	$0.699108\pi$
$38$	2.29618	+	0.746074i	0.372490	+	0.121029i
$39$	2.87468	+	11.3597i	0.460317	+	1.81901i
$40$	0.309017	+	0.951057i	0.0488599	+	0.150375i
$41$	−4.40895	−	6.06840i	−0.688562	−	0.947724i	0.311435	−	0.950268i	$-0.399190\pi$
$41$	−4.40895	−	6.06840i	−0.688562	−	0.947724i	−0.999997	+	0.00254313i	$0.999190\pi$
$42$	−0.175222	+	0.438110i	−0.0270373	+	0.0676018i
$43$	1.26819	+	1.74551i	0.193397	+	0.266188i	0.894693	−	0.446683i	$-0.147395\pi$
$43$	1.26819	+	1.74551i	0.193397	+	0.266188i	−0.701296	+	0.712871i	$0.747395\pi$
$44$	0.465165	+	0.337962i	0.0701262	+	0.0509497i
$45$	−2.95069	+	0.541668i	−0.439864	+	0.0807471i
$46$	−3.11150	+	4.28262i	−0.458766	+	0.631437i
$47$	7.33436	−	10.0949i	1.06983	−	1.47249i	0.199575	−	0.979883i	$-0.436044\pi$
$47$	7.33436	−	10.0949i	1.06983	−	1.47249i	0.870252	−	0.492607i	$-0.163956\pi$
$48$	1.67912	−	0.424916i	0.242360	−	0.0613314i
$49$	5.60308	+	4.07087i	0.800440	+	0.581554i
$50$	−0.587785	−	0.809017i	−0.0831254	−	0.114412i
$51$	9.50539	+	3.80168i	1.33102	+	0.532341i
$52$	3.97653	+	5.47323i	0.551446	+	0.759000i
$53$	−3.15692	−	9.71600i	−0.433636	−	1.33460i	−0.894478	−	0.447113i	$-0.852452\pi$
$53$	−3.15692	−	9.71600i	−0.433636	−	1.33460i	0.460841	−	0.887483i	$-0.347548\pi$
$54$	0.597520	+	5.16168i	0.0813122	+	0.702416i
$55$	−0.546834	−	0.177677i	−0.0737351	−	0.0239580i
$56$			0.272423i			0.0364041i
$57$	−0.277064	+	4.17258i	−0.0366981	+	0.552672i
$58$	−2.31887	−	0.753446i	−0.304482	−	0.0989323i
$59$	−7.48784	+	10.3061i	−0.974834	+	1.34174i	−0.0352676	+	0.999378i	$0.511228\pi$
$59$	−7.48784	+	10.3061i	−0.974834	+	1.34174i	−0.939567	+	0.342366i	$0.888772\pi$
$60$	−1.46563	+	0.922996i	−0.189212	+	0.119158i
$61$		−	10.5251i		−	1.34760i	−0.738914	−	0.673799i	$-0.764661\pi$
$61$		−	10.5251i		−	1.34760i	0.738914	−	0.673799i	$-0.235339\pi$
$62$	4.98319	−	2.48351i	0.632866	−	0.315406i
$63$	−0.810094	−	0.108059i	−0.102062	−	0.0136141i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−5.47323	−	3.97653i	−0.678870	−	0.493228i
$66$	−0.369823	+	0.924673i	−0.0455220	+	0.113819i
$67$	9.75486			1.19175			0.595873	−	0.803079i	$-0.296806\pi$
$67$	9.75486			1.19175			0.595873	+	0.803079i	$0.296806\pi$
$68$	5.91059			0.716764
$69$	−8.51316	−	3.40484i	−1.02486	−	0.409894i
$70$	−0.0841834	−	0.259090i	−0.0100618	−	0.0309671i
$71$	−4.16863	+	1.35447i	−0.494725	+	0.160746i	−0.545744	−	0.837952i	$-0.683753\pi$
$71$	−4.16863	+	1.35447i	−0.494725	+	0.160746i	0.0510193	+	0.998698i	$0.483753\pi$
$72$	1.42697	+	2.63889i	0.168170	+	0.310996i
$73$	11.2674	+	3.66099i	1.31874	+	0.428486i	0.882064	−	0.471131i	$-0.156154\pi$
$73$	11.2674	+	3.66099i	1.31874	+	0.428486i	0.436681	+	0.899617i	$0.356154\pi$
$74$	−7.97862	+	5.79681i	−0.927496	+	0.673865i
$75$	1.10868	−	1.33073i	0.128019	−	0.153659i
$76$	0.746074	+	2.29618i	0.0855806	+	0.263390i
$77$	−0.126722	−	0.0920686i	−0.0144413	−	0.0104922i
$78$	−7.50051	+	9.00274i	−0.849266	+	1.01936i
$79$	−5.47101	+	1.77764i	−0.615537	+	0.200000i	−0.600158	−	0.799882i	$-0.704896\pi$
$79$	−5.47101	+	1.77764i	−0.615537	+	0.200000i	−0.0153793	+	0.999882i	$0.504896\pi$
$80$	−0.587785	+	0.809017i	−0.0657164	+	0.0904508i
$81$	−8.41319	+	3.19659i	−0.934799	+	0.355177i
$82$	2.31792	−	7.13383i	0.255972	−	0.787800i
$83$	7.86138	−	5.71163i	0.862899	−	0.626933i	−0.0657732	−	0.997835i	$-0.520951\pi$
$83$	7.86138	−	5.71163i	0.862899	−	0.626933i	0.928672	+	0.370902i	$0.120951\pi$
$84$	−0.457431	+	0.115757i	−0.0499098	+	0.0126301i
$85$	−5.62130	+	1.82647i	−0.609716	+	0.198109i
$86$	−0.666726	+	2.05197i	−0.0718949	+	0.221270i
$87$	0.279802	−	4.21381i	0.0299979	−	0.451768i
$88$			0.574975i			0.0612926i
$89$	−4.69430	+	14.4476i	−0.497595	+	1.53144i	0.315279	+	0.948999i	$0.397902\pi$
$89$	−4.69430	+	14.4476i	−0.497595	+	1.53144i	−0.812874	+	0.582440i	$0.802098\pi$
$90$	−2.17259	−	2.06878i	−0.229011	−	0.218068i
$91$	−1.08330	−	1.49103i	−0.113561	−	0.156303i
$92$	−5.29360			−0.551896
$93$	6.28755	+	7.31209i	0.651989	+	0.758229i
$94$	12.4780			1.28700
$95$	−1.41912	−	1.95325i	−0.145598	−	0.200399i
$96$	1.33073	+	1.10868i	0.135817	+	0.113154i
$97$	0.889534	−	2.73770i	0.0903185	−	0.277972i	−0.895687	−	0.444685i	$-0.853316\pi$
$97$	0.889534	−	2.73770i	0.0903185	−	0.277972i	0.986005	+	0.166714i	$0.0533155\pi$
$98$			6.92579i			0.699610i
$99$	−1.70978	−	0.228069i	−0.171840	−	0.0229218i
$100$	0.309017	−	0.951057i	0.0309017	−	0.0951057i
$101$	11.5306	−	3.74652i	1.14734	−	0.372793i	0.327198	−	0.944956i	$-0.393895\pi$
$101$	11.5306	−	3.74652i	1.14734	−	0.372793i	0.820140	+	0.572163i	$0.193895\pi$
$102$	2.51150	+	9.92459i	0.248676	+	0.982681i
$103$	−0.119088	+	0.0865226i	−0.0117341	+	0.00852532i	−0.593637	−	0.804733i	$-0.702308\pi$
$103$	−0.119088	+	0.0865226i	−0.0117341	+	0.00852532i	0.581903	+	0.813258i	$0.302308\pi$
$104$	−2.09059	+	6.43416i	−0.204999	+	0.630922i
$105$	0.399272	−	0.251445i	0.0389650	−	0.0245386i
$106$	6.00482	−	8.26492i	0.583240	−	0.802760i
$107$	1.96127	−	0.637255i	0.189603	−	0.0616057i	−0.212676	−	0.977123i	$-0.568218\pi$
$107$	1.96127	−	0.637255i	0.189603	−	0.0616057i	0.402279	+	0.915517i	$0.368218\pi$
$108$	−3.82468	+	3.51737i	−0.368030	+	0.338459i
$109$	−3.65032	−	2.65211i	−0.349637	−	0.254026i	0.399080	−	0.916916i	$-0.369330\pi$
$109$	−3.65032	−	2.65211i	−0.349637	−	0.254026i	−0.748717	+	0.662890i	$0.769330\pi$
$110$	−0.177677	−	0.546834i	−0.0169408	−	0.0521386i
$111$	−13.1238	−	10.9339i	−1.24566	−	1.03780i
$112$	−0.220395	+	0.160126i	−0.0208254	+	0.0151305i
$113$	−9.15830	−	2.97571i	−0.861541	−	0.279931i	−0.155269	−	0.987872i	$-0.549624\pi$
$113$	−9.15830	−	2.97571i	−0.861541	−	0.279931i	−0.706272	+	0.707941i	$0.749624\pi$
$114$	−3.53855	+	2.22843i	−0.331415	+	0.208712i
$115$	5.03452	−	1.63581i	0.469471	−	0.152540i
$116$	−0.753446	−	2.31887i	−0.0699557	−	0.215301i
$117$	−18.3038	−	8.76886i	−1.69218	−	0.810681i
$118$	−12.7391			−1.17273
$119$	−1.61018			−0.147605
$120$	−1.60820	−	0.643198i	−0.146808	−	0.0587157i
$121$	8.63173	+	6.27132i	0.784703	+	0.570120i
$122$	8.51497	−	6.18649i	0.770909	−	0.560098i
$123$	12.9635	+	0.860790i	1.16888	+	0.0776148i
$124$	4.93825	+	2.57172i	0.443468	+	0.230947i
$125$			1.00000i			0.0894427i
$126$	−0.388740	−	0.718895i	−0.0346317	−	0.0640443i
$127$	12.0711	−	16.6145i	1.07114	−	1.47430i	0.202224	−	0.979339i	$-0.435183\pi$
$127$	12.0711	−	16.6145i	1.07114	−	1.47430i	0.868916	−	0.494959i	$-0.164817\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	−3.72881	−	0.247597i	−0.328304	−	0.0217997i
$130$		−	6.76528i		−	0.593354i
$131$	−13.9409	−	4.52968i	−1.21802	−	0.395760i	−0.371661	−	0.928368i	$-0.621212\pi$
$131$	−13.9409	−	4.52968i	−1.21802	−	0.395760i	−0.846362	+	0.532609i	$0.821212\pi$
$132$	−0.965453	+	0.244316i	−0.0840319	+	0.0212650i
$133$	−0.203248	−	0.625533i	−0.0176238	−	0.0542406i
$134$	5.73376	+	7.89184i	0.495321	+	0.681751i
$135$	2.55056	−	4.52710i	0.219517	−	0.389631i
$136$	3.47416	+	4.78177i	0.297906	+	0.410033i
$137$	−2.83623	−	2.06064i	−0.242315	−	0.176052i	0.459999	−	0.887919i	$-0.347850\pi$
$137$	−2.83623	−	2.06064i	−0.242315	−	0.176052i	−0.702314	+	0.711867i	$0.747850\pi$
$138$	−2.24934	−	8.88860i	−0.191476	−	0.756648i
$139$	−5.77462	+	7.94809i	−0.489797	+	0.674148i	−0.980351	−	0.197263i	$-0.936795\pi$
$139$	−5.77462	+	7.94809i	−0.489797	+	0.674148i	0.490553	+	0.871411i	$0.336795\pi$
$140$	0.160126	−	0.220395i	0.0135331	−	0.0186268i
$141$	5.30209	+	20.9520i	0.446516	+	1.76448i
$142$	−3.54605	−	2.57635i	−0.297578	−	0.216203i
$143$	−2.28641	−	3.14697i	−0.191199	−	0.263163i
$144$	−1.29616	+	2.70555i	−0.108013	+	0.225462i
$145$	1.43314	+	1.97255i	0.119016	+	0.163811i
$146$	3.66099	+	11.2674i	0.302985	+	0.932493i
$147$	−11.6292	+	2.94288i	−0.959163	+	0.242725i
$148$	−9.37944	−	3.04756i	−0.770985	−	0.250508i
$149$		−	5.35932i		−	0.439053i	−0.975607	−	0.219526i	$-0.929549\pi$
$149$		−	5.35932i		−	0.439053i	0.975607	−	0.219526i	$-0.0704512\pi$
$150$	1.72824	+	0.114757i	0.141111	+	0.00936991i
$151$	−5.27676	−	1.71452i	−0.429417	−	0.139526i	0.0863309	−	0.996267i	$-0.472486\pi$
$151$	−5.27676	−	1.71452i	−0.429417	−	0.139526i	−0.515748	+	0.856741i	$0.672486\pi$
$152$	−1.41912	+	1.95325i	−0.115106	+	0.158429i
$153$	−15.5974	+	8.43424i	−1.26098	+	0.681868i
$154$		−	0.156637i		−	0.0126221i
$155$	−5.49126	−	0.919844i	−0.441068	−	0.0738837i
$156$	−11.6921	−	0.776366i	−0.936114	−	0.0621590i
$157$	−9.92446	+	7.21054i	−0.792058	+	0.575464i	−0.908573	−	0.417725i	$-0.862828\pi$
$157$	−9.92446	+	7.21054i	−0.792058	+	0.575464i	0.116515	+	0.993189i	$0.462828\pi$
$158$	−4.65392	−	3.38127i	−0.370246	−	0.269000i
$159$	16.4293	+	6.57091i	1.30293	+	0.521107i
$160$	−1.00000			−0.0790569
$161$	1.44210			0.113653
$162$	−7.53125	−	4.92751i	−0.591711	−	0.387141i
$163$	−2.71134	−	8.34464i	−0.212368	−	0.653602i	−0.999330	−	0.0366006i	$-0.988347\pi$
$163$	−2.71134	−	8.34464i	−0.212368	−	0.653602i	0.786962	−	0.617002i	$-0.211653\pi$
$164$	7.13383	−	2.31792i	0.557058	−	0.180999i
$165$	0.842702	−	0.530700i	0.0656043	−	0.0413149i
$166$	9.24161	+	3.00278i	0.717288	+	0.233061i
$167$	2.32193	−	1.68698i	0.179676	−	0.130542i	−0.494312	−	0.869285i	$-0.664580\pi$
$167$	2.32193	−	1.68698i	0.179676	−	0.130542i	0.673988	+	0.738742i	$0.264580\pi$
$168$	−0.362521	−	0.302029i	−0.0279691	−	0.0233021i
$169$	−10.1262	−	31.1652i	−0.778937	−	2.39732i
$170$	−4.78177	−	3.47416i	−0.366745	−	0.266456i
$171$	−5.24539	−	4.99475i	−0.401125	−	0.381958i
$172$	−2.05197	+	0.666726i	−0.156461	+	0.0508374i
$173$	−3.91051	+	5.38236i	−0.297311	+	0.409213i	−0.931372	−	0.364070i	$-0.881387\pi$
$173$	−3.91051	+	5.38236i	−0.297311	+	0.409213i	0.634061	+	0.773283i	$0.281387\pi$
$174$	3.57351	−	2.25045i	0.270907	−	0.170606i
$175$	−0.0841834	+	0.259090i	−0.00636366	+	0.0195853i
$176$	−0.465165	+	0.337962i	−0.0350631	+	0.0254748i
$177$	−5.41304	−	21.3905i	−0.406869	−	1.60780i
$178$	−14.4476	+	4.69430i	−1.08289	+	0.351853i
$179$	2.31705	−	7.13114i	0.173184	−	0.533006i	−0.826362	−	0.563140i	$-0.809593\pi$
$179$	2.31705	−	7.13114i	0.173184	−	0.533006i	0.999546	+	0.0301336i	$0.00959328\pi$
$180$	0.396658	−	2.97366i	0.0295651	−	0.221644i
$181$		−	21.5693i		−	1.60324i	−0.597837	−	0.801618i	$-0.703973\pi$
$181$		−	21.5693i		−	1.60324i	0.597837	−	0.801618i	$-0.296027\pi$
$182$	0.569524	−	1.75281i	0.0422159	−	0.129927i
$183$	14.0060	+	11.6689i	1.03535	+	0.862592i
$184$	−3.11150	−	4.28262i	−0.229383	−	0.315719i
$185$	9.86212			0.725078
$186$	−2.21988	+	9.38468i	−0.162769	+	0.688118i
$187$	−3.39844			−0.248519
$188$	7.33436	+	10.0949i	0.534913	+	0.736245i
$189$	1.04193	−	0.958212i	0.0757892	−	0.0696996i
$190$	0.746074	−	2.29618i	0.0541259	−	0.166582i
$191$		−	6.34878i		−	0.459381i	−0.973264	−	0.229691i	$-0.926229\pi$
$191$		−	6.34878i		−	0.459381i	0.973264	−	0.229691i	$-0.0737715\pi$
$192$	−0.114757	+	1.72824i	−0.00828191	+	0.124725i
$193$	2.75980	−	8.49380i	0.198655	−	0.611397i	−0.801259	−	0.598317i	$-0.795836\pi$
$193$	2.75980	−	8.49380i	0.198655	−	0.611397i	0.999914	−	0.0130801i	$-0.00416366\pi$
$194$	2.73770	−	0.889534i	0.196556	−	0.0638648i
$195$	11.3597	−	2.87468i	0.813486	−	0.205860i
$196$	−5.60308	+	4.07087i	−0.400220	+	0.290777i
$197$	3.37007	−	10.3720i	0.240107	−	0.738975i	−0.756295	−	0.654230i	$-0.772993\pi$
$197$	3.37007	−	10.3720i	0.240107	−	0.738975i	0.996403	−	0.0847442i	$-0.0270073\pi$
$198$	−0.820473	−	1.51730i	−0.0583085	−	0.107830i
$199$	−7.79987	+	10.7356i	−0.552918	+	0.761027i	−0.990405	−	0.138198i	$-0.955869\pi$
$199$	−7.79987	+	10.7356i	−0.552918	+	0.761027i	0.437486	+	0.899225i	$0.355869\pi$
$200$	0.951057	−	0.309017i	0.0672499	−	0.0218508i
$201$	−10.8150	+	12.9810i	−0.762831	+	0.915613i
$202$	9.80852	+	7.12631i	0.690125	+	0.501405i
$203$	0.205256	+	0.631713i	0.0144061	+	0.0443376i
$204$	−6.55294	+	7.86538i	−0.458797	+	0.550687i
$205$	−6.06840	+	4.40895i	−0.423835	+	0.307934i
$206$	−0.139996	−	0.0454876i	−0.00975402	−	0.00316927i
$207$	13.9693	−	7.55382i	0.970930	−	0.525027i
$208$	−6.43416	+	2.09059i	−0.446129	+	0.144956i
$209$	−0.428974	−	1.32025i	−0.0296728	−	0.0913234i
$210$	0.438110	+	0.175222i	0.0302325	+	0.0120915i
$211$	−7.31822			−0.503807			−0.251904	−	0.967752i	$-0.581057\pi$
$211$	−7.31822			−0.503807			−0.251904	+	0.967752i	$0.581057\pi$
$212$	10.2160			0.701638
$213$	2.81924	−	7.04897i	0.193171	−	0.482988i
$214$	1.66835	+	1.21213i	0.114046	+	0.0828595i
$215$	1.74551	−	1.26819i	0.119043	−	0.0864897i
$216$	−5.09370	−	1.02677i	−0.346582	−	0.0698630i
$217$	−1.34529	−	0.700595i	−0.0913244	−	0.0475595i
$218$		−	4.51204i		−	0.305594i
$219$	−17.3636	+	10.9349i	−1.17333	+	0.738913i
$220$	0.337962	−	0.465165i	0.0227854	−	0.0313614i
$221$	−38.0297	−	12.3566i	−2.55815	−	0.831194i
$222$	1.13175	−	17.0442i	0.0759582	−	1.14393i
$223$			20.2280i			1.35457i	0.735722	+	0.677284i	$0.236843\pi$
$223$			20.2280i			1.35457i	−0.735722	+	0.677284i	$0.763157\pi$
$224$	−0.259090	−	0.0841834i	−0.0173112	−	0.00562474i
$225$	0.541668	+	2.95069i	0.0361112	+	0.196713i
$226$	−2.97571	−	9.15830i	−0.197941	−	0.609201i
$227$	1.80469	+	2.48394i	0.119781	+	0.164865i	0.864697	−	0.502294i	$-0.167510\pi$
$227$	1.80469	+	2.48394i	0.119781	+	0.164865i	−0.744916	+	0.667158i	$0.767510\pi$
$228$	−3.88275	−	1.55290i	−0.257141	−	0.102844i
$229$	16.0074	+	22.0323i	1.05780	+	1.45593i	0.881848	+	0.471534i	$0.156300\pi$
$229$	16.0074	+	22.0323i	1.05780	+	1.45593i	0.175950	+	0.984399i	$0.443700\pi$
$230$	4.28262	+	3.11150i	0.282387	+	0.205166i
$231$	0.263012	−	0.0665574i	0.0173049	−	0.00437916i
$232$	1.43314	−	1.97255i	0.0940902	−	0.129504i
$233$	−13.0839	+	18.0084i	−0.857155	+	1.17977i	0.125085	+	0.992146i	$0.460080\pi$
$233$	−13.0839	+	18.0084i	−0.857155	+	1.17977i	−0.982240	+	0.187627i	$0.939920\pi$
$234$	−3.66453	−	19.9623i	−0.239558	−	1.30497i
$235$	−10.0949	−	7.33436i	−0.658517	−	0.478441i
$236$	−7.48784	−	10.3061i	−0.487417	−	0.670872i
$237$	3.70004	−	9.25125i	0.240343	−	0.600934i
$238$	−0.946440	−	1.30266i	−0.0613486	−	0.0844391i
$239$	6.70715	+	20.6425i	0.433850	+	1.33525i	0.894261	+	0.447546i	$0.147702\pi$
$239$	6.70715	+	20.6425i	0.433850	+	1.33525i	−0.460411	+	0.887706i	$0.652298\pi$
$240$	−0.424916	−	1.67912i	−0.0274282	−	0.108387i
$241$	1.13921	+	0.370152i	0.0733830	+	0.0238436i	0.345478	−	0.938427i	$-0.387717\pi$
$241$	1.13921	+	0.370152i	0.0733830	+	0.0238436i	−0.272095	+	0.962270i	$0.587717\pi$
$242$			10.6694i			0.685855i
$243$	5.07373	−	14.7397i	0.325480	−	0.945549i
$244$	10.0099	+	3.25243i	0.640821	+	0.208215i
$245$	4.07087	−	5.60308i	0.260079	−	0.357968i
$246$	6.92335	+	10.9936i	0.441417	+	0.700929i
$247$		−	16.3337i		−	1.03929i
$248$	0.822067	+	5.50674i	0.0522013	+	0.349678i
$249$	−1.11512	+	16.7937i	−0.0706680	+	1.06426i
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	15.7948	+	11.4756i	0.996962	+	0.724335i	0.961435	−	0.275034i	$-0.0886890\pi$
$251$	15.7948	+	11.4756i	0.996962	+	0.724335i	0.0355272	+	0.999369i	$0.488689\pi$
$252$	0.353103	−	0.737053i	0.0222434	−	0.0464300i
$253$	3.04369			0.191355
$254$	20.5366			1.28858
$255$	3.80168	−	9.50539i	0.238070	−	0.595250i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−12.9290	+	4.20089i	−0.806490	+	0.262044i	−0.683110	−	0.730315i	$-0.739373\pi$
$257$	−12.9290	+	4.20089i	−0.806490	+	0.262044i	−0.123379	+	0.992360i	$0.539373\pi$
$258$	−1.99143	−	3.16221i	−0.123981	−	0.196870i
$259$	2.55517	+	0.830227i	0.158771	+	0.0515878i
$260$	5.47323	−	3.97653i	0.339435	−	0.246614i
$261$	5.29722	+	5.04410i	0.327890	+	0.312222i
$262$	−4.52968	−	13.9409i	−0.279844	−	0.861272i
$263$	24.4841	+	17.7887i	1.50975	+	1.09690i	0.966287	+	0.257467i	$0.0828879\pi$
$263$	24.4841	+	17.7887i	1.50975	+	1.09690i	0.543465	+	0.839432i	$0.317112\pi$
$264$	−0.765135	−	0.637462i	−0.0470908	−	0.0392331i
$265$	−9.71600	+	3.15692i	−0.596849	+	0.193928i
$266$	0.386600	−	0.532110i	0.0237040	−	0.0326257i
$267$	−14.0213	−	22.2645i	−0.858090	−	1.36257i
$268$	−3.01442	+	9.27742i	−0.184135	+	0.566709i
$269$	−13.1662	+	9.56581i	−0.802758	+	0.583238i	−0.911722	−	0.410808i	$-0.865247\pi$
$269$	−13.1662	+	9.56581i	−0.802758	+	0.583238i	0.108964	+	0.994046i	$0.465247\pi$
$270$	5.16168	−	0.597520i	0.314130	−	0.0363639i
$271$	−3.42289	+	1.11217i	−0.207926	+	0.0675593i	−0.411128	−	0.911578i	$-0.634865\pi$
$271$	−3.42289	+	1.11217i	−0.207926	+	0.0675593i	0.203202	+	0.979137i	$0.434865\pi$
$272$	−1.82647	+	5.62130i	−0.110746	+	0.340842i
$273$	3.18519	+	0.211500i	0.192776	+	0.0128006i
$274$		−	3.50577i		−	0.211791i
$275$	−0.177677	+	0.546834i	−0.0107143	+	0.0329753i
$276$	5.86890	−	7.04434i	0.353266	−	0.424020i
$277$	11.2011	+	15.4171i	0.673012	+	0.926321i	0.999824	−	0.0187683i	$-0.00597448\pi$
$277$	11.2011	+	15.4171i	0.673012	+	0.926321i	−0.326812	+	0.945089i	$0.605974\pi$
$278$	−9.82438			−0.589227
$279$	−16.7013	+	0.260256i	−0.999879	+	0.0155811i
$280$	0.272423			0.0162804
$281$	−0.237292	−	0.326604i	−0.0141556	−	0.0194835i	0.801881	−	0.597484i	$-0.203833\pi$
$281$	−0.237292	−	0.326604i	−0.0141556	−	0.0194835i	−0.816036	+	0.578001i	$0.803833\pi$
$282$	−13.8340	+	16.6048i	−0.823805	+	0.988799i
$283$	3.76791	−	11.5964i	0.223979	−	0.689336i	−0.774415	−	0.632678i	$-0.781956\pi$
$283$	3.76791	−	11.5964i	0.223979	−	0.689336i	0.998394	−	0.0566581i	$-0.0180445\pi$
$284$		−	4.38315i		−	0.260092i
$285$	4.17258	+	0.277064i	0.247163	+	0.0164119i
$286$	1.20204	−	3.69948i	0.0710778	−	0.218755i
$287$	−1.94342	+	0.631455i	−0.114716	+	0.0372736i
$288$	−2.95069	+	0.541668i	−0.173871	+	0.0319181i
$289$	−14.5098	+	10.5420i	−0.853515	+	0.620115i
$290$	−0.753446	+	2.31887i	−0.0442439	+	0.136169i
$291$	2.65693	+	4.21896i	0.155752	+	0.247320i
$292$	−6.96361	+	9.58459i	−0.407514	+	0.560895i
$293$	30.0501	−	9.76386i	1.75554	−	0.570411i	0.758821	−	0.651299i	$-0.225776\pi$
$293$	30.0501	−	9.76386i	1.75554	−	0.570411i	0.996723	+	0.0808880i	$0.0257756\pi$
$294$	−9.21633	−	7.67846i	−0.537507	−	0.447817i
$295$	10.3061	+	7.48784i	0.600046	+	0.435959i
$296$	−3.04756	−	9.37944i	−0.177136	−	0.545169i
$297$	2.19909	−	2.02240i	0.127604	−	0.117351i
$298$	4.33578	−	3.15013i	0.251165	−	0.182482i
$299$	34.0599	+	11.0667i	1.96974	+	0.640006i
$300$	0.922996	+	1.46563i	0.0532892	+	0.0846183i
$301$	0.559005	−	0.181632i	0.0322205	−	0.0104691i
$302$	−1.71452	−	5.27676i	−0.0986598	−	0.303644i
$303$	−7.79813	+	19.4978i	−0.447991	+	1.12012i
$304$	−2.41435			−0.138472
$305$	−10.5251			−0.602664
$306$	−15.9914	−	7.66104i	−0.914166	−	0.437953i
$307$	−4.70346	−	3.41726i	−0.268441	−	0.195034i	0.445419	−	0.895322i	$-0.353055\pi$
$307$	−4.70346	−	3.41726i	−0.268441	−	0.195034i	−0.713860	+	0.700289i	$0.753055\pi$
$308$	0.126722	−	0.0920686i	0.00722063	−	0.00524610i
$309$	0.0168924	−	0.254399i	0.000960976	−	0.0144723i
$310$	−2.48351	−	4.98319i	−0.141054	−	0.283026i
$311$			11.0311i			0.625515i	0.949833	+	0.312758i	$0.101253\pi$
$311$			11.0311i			0.625515i	−0.949833	+	0.312758i	$0.898747\pi$
$312$	−6.24433	−	9.91541i	−0.353515	−	0.561350i
$313$	−0.259803	+	0.357588i	−0.0146849	+	0.0202121i	−0.816296	−	0.577633i	$-0.803976\pi$
$313$	−0.259803	+	0.357588i	−0.0146849	+	0.0202121i	0.801611	+	0.597845i	$0.203976\pi$
$314$	−11.6669	−	3.79081i	−0.658401	−	0.213928i
$315$	−0.108059	+	0.810094i	−0.00608842	+	0.0456436i
$316$		−	5.75256i		−	0.323607i
$317$	−2.34400	−	0.761611i	−0.131652	−	0.0427763i	0.242450	−	0.970164i	$-0.422049\pi$
$317$	−2.34400	−	0.761611i	−0.131652	−	0.0427763i	−0.374102	+	0.927388i	$0.622049\pi$
$318$	4.34095	+	17.1539i	0.243428	+	0.961943i
$319$	0.433213	+	1.33329i	0.0242553	+	0.0746500i
$320$	−0.587785	−	0.809017i	−0.0328582	−	0.0452254i
$321$	−1.32640	+	3.31642i	−0.0740325	+	0.185105i
$322$	0.847645	+	1.16668i	0.0472374	+	0.0650167i
$323$	−11.5448	−	8.38782i	−0.642372	−	0.466711i
$324$	−0.440320	−	8.98922i	−0.0244622	−	0.499401i
$325$	−3.97653	+	5.47323i	−0.220578	+	0.303600i
$326$	5.15727	−	7.09837i	0.285635	−	0.393143i
$327$	7.57626	−	1.91724i	0.418968	−	0.106024i
$328$	6.06840	+	4.40895i	0.335071	+	0.243443i
$329$	−1.99805	−	2.75008i	−0.110156	−	0.151617i
$330$	0.924673	+	0.369823i	0.0509016	+	0.0203581i
$331$	18.1780	+	25.0198i	0.999151	+	1.37521i	0.925845	+	0.377904i	$0.123355\pi$
$331$	18.1780	+	25.0198i	0.999151	+	1.37521i	0.0733066	+	0.997309i	$0.476645\pi$
$332$	3.00278	+	9.24161i	0.164799	+	0.507199i
$333$	29.1001	−	5.34199i	1.59468	−	0.292739i
$334$	2.72959	+	0.886897i	0.149356	+	0.0485288i
$335$		−	9.75486i		−	0.532965i
$336$	0.0312626	−	0.470814i	0.00170551	−	0.0256850i
$337$	−0.372547	−	0.121048i	−0.0202939	−	0.00659390i	0.298852	−	0.954299i	$-0.403396\pi$
$337$	−0.372547	−	0.121048i	−0.0202939	−	0.00659390i	−0.319146	+	0.947705i	$0.603396\pi$
$338$	19.2611	−	26.5107i	1.04767	−	1.44199i
$339$	14.1135	−	8.88809i	0.766538	−	0.482735i
$340$		−	5.91059i		−	0.320547i
$341$	−2.83937	−	1.47867i	−0.153760	−	0.0800746i
$342$	0.957670	−	7.17945i	0.0517849	−	0.388220i
$343$	3.06917	−	2.22988i	0.165720	−	0.120402i
$344$	−1.74551	−	1.26819i	−0.0941117	−	0.0683761i
$345$	−3.40484	+	8.51316i	−0.183310	+	0.458333i
$346$	−6.65296			−0.357665
$347$	20.4773			1.09928			0.549640	−	0.835401i	$-0.314765\pi$
$347$	20.4773			1.09928			0.549640	+	0.835401i	$0.314765\pi$
$348$	3.92111	+	1.56825i	0.210193	+	0.0840668i
$349$	−6.38250	−	19.6433i	−0.341647	−	1.05148i	−0.963354	−	0.268233i	$-0.913560\pi$
$349$	−6.38250	−	19.6433i	−0.341647	−	1.05148i	0.621707	−	0.783250i	$-0.286440\pi$
$350$	−0.259090	+	0.0841834i	−0.0138489	+	0.00449979i
$351$	31.9619	−	14.6355i	1.70600	−	0.781184i
$352$	−0.546834	−	0.177677i	−0.0291463	−	0.00947022i
$353$	−19.7050	+	14.3165i	−1.04879	+	0.761990i	−0.971982	−	0.235056i	$-0.924473\pi$
$353$	−19.7050	+	14.3165i	−1.04879	+	0.761990i	−0.0768072	+	0.997046i	$0.524473\pi$
$354$	14.1235	−	16.9522i	0.750657	−	0.901001i
$355$	1.35447	+	4.16863i	0.0718878	+	0.221248i
$356$	−12.2898	−	8.92909i	−0.651360	−	0.473241i
$357$	1.78517	−	2.14271i	0.0944813	−	0.113404i
$358$	7.13114	−	2.31705i	0.376892	−	0.122460i
$359$	−18.0363	+	24.8248i	−0.951918	+	1.31020i	−0.00124802	+	0.999999i	$0.500397\pi$
$359$	−18.0363	+	24.8248i	−0.951918	+	1.31020i	−0.950670	+	0.310204i	$0.899603\pi$
$360$	2.63889	−	1.42697i	0.139082	−	0.0752080i
$361$	−4.07004	+	12.5263i	−0.214213	+	0.659279i
$362$	17.4499	−	12.6781i	0.917149	−	0.666348i
$363$	−17.9152	+	4.53360i	−0.940305	+	0.237952i
$364$	1.75281	−	0.569524i	0.0918724	−	0.0298512i
$365$	3.66099	−	11.2674i	0.191625	−	0.589760i
$366$	−1.20783	+	18.1899i	−0.0631344	+	0.950802i
$367$			31.2674i			1.63215i	0.577949	+	0.816073i	$0.303853\pi$
$367$			31.2674i			1.63215i	−0.577949	+	0.816073i	$0.696147\pi$
$368$	1.63581	−	5.03452i	0.0852727	−	0.262442i
$369$	−15.5178	+	16.2965i	−0.807824	+	0.848363i
$370$	5.79681	+	7.97862i	0.301362	+	0.414789i
$371$	−2.78308			−0.144490
$372$	−8.89717	+	3.72025i	−0.461297	+	0.192886i
$373$	−10.1885			−0.527540			−0.263770	−	0.964586i	$-0.584966\pi$
$373$	−10.1885			−0.527540			−0.263770	+	0.964586i	$0.584966\pi$
$374$	−1.99755	−	2.74940i	−0.103291	−	0.142168i
$375$	−1.33073	−	1.10868i	−0.0687184	−	0.0572519i
$376$	−3.85590	+	11.8672i	−0.198853	+	0.612006i
$377$			16.4951i			0.849542i
$378$	1.38764	+	0.279716i	0.0713725	+	0.0143871i
$379$	10.2591	−	31.5742i	0.526974	−	1.62186i	−0.233405	−	0.972380i	$-0.574987\pi$
$379$	10.2591	−	31.5742i	0.526974	−	1.62186i	0.760379	−	0.649480i	$-0.225013\pi$
$380$	2.29618	−	0.746074i	0.117792	−	0.0382728i
$381$	8.72635	+	34.4835i	0.447065	+	1.76664i
$382$	5.13627	−	3.73172i	0.262794	−	0.190931i
$383$	−6.57595	+	20.2387i	−0.336015	+	1.03415i	0.630204	+	0.776429i	$0.282971\pi$
$383$	−6.57595	+	20.2387i	−0.336015	+	1.03415i	−0.966220	+	0.257720i	$0.917029\pi$
$384$	−1.46563	+	0.922996i	−0.0747927	+	0.0471015i
$385$	−0.0920686	+	0.126722i	−0.00469225	+	0.00645833i
$386$	8.49380	−	2.75980i	0.432323	−	0.140470i
$387$	4.46353	−	4.68752i	0.226894	−	0.238280i
$388$	2.32883	+	1.69199i	0.118228	+	0.0858980i
$389$	−0.493699	−	1.51945i	−0.0250315	−	0.0770391i	0.937760	−	0.347283i	$-0.112896\pi$
$389$	−0.493699	−	1.51945i	−0.0250315	−	0.0770391i	−0.962792	+	0.270244i	$0.912896\pi$
$390$	9.00274	+	7.50051i	0.455871	+	0.379803i
$391$	25.3128	−	18.3908i	1.28012	−	0.930063i
$392$	−6.58681	−	2.14019i	−0.332684	−	0.108096i
$393$	21.4837	−	13.5296i	1.08371	−	0.682478i
$394$	10.3720	−	3.37007i	0.522534	−	0.169782i
$395$	1.77764	+	5.47101i	0.0894428	+	0.275277i
$396$	0.745258	−	1.55562i	0.0374506	−	0.0781729i
$397$	−13.9033			−0.697788			−0.348894	−	0.937162i	$-0.613443\pi$
$397$	−13.9033			−0.697788			−0.348894	+	0.937162i	$0.613443\pi$
$398$	−13.2699			−0.665162
$399$	1.05775	+	0.423047i	0.0529537	+	0.0211788i
$400$	0.809017	+	0.587785i	0.0404508	+	0.0293893i
$401$	−27.4172	+	19.9197i	−1.36915	+	0.994744i	−0.371345	+	0.928495i	$0.621103\pi$
$401$	−27.4172	+	19.9197i	−1.36915	+	0.994744i	−0.997803	+	0.0662494i	$0.978897\pi$
$402$	−16.8588	−	1.11944i	−0.840840	−	0.0558327i
$403$	−26.3971	−	26.8707i	−1.31493	−	1.33852i
$404$			12.1240i			0.603192i
$405$	3.19659	+	8.41319i	0.158840	+	0.418055i
$406$	−0.390420	+	0.537367i	−0.0193762	+	0.0266691i
$407$	5.39294	+	1.75227i	0.267318	+	0.0868570i
$408$	−10.2149	−	0.678284i	−0.505715	−	0.0335801i
$409$			2.33373i			0.115396i	0.998334	+	0.0576979i	$0.0183760\pi$
$409$			2.33373i			0.115396i	−0.998334	+	0.0576979i	$0.981624\pi$
$410$	−7.13383	−	2.31792i	−0.352315	−	0.114474i
$411$	5.88661	−	1.48966i	0.290365	−	0.0734794i
$412$	−0.0454876	−	0.139996i	−0.00224101	−	0.00689713i
$413$	2.03986	+	2.80763i	0.100375	+	0.138154i
$414$	14.3221	+	6.86134i	0.703892	+	0.337216i
$415$	−5.71163	−	7.86138i	−0.280373	−	0.385900i
$416$	−5.47323	−	3.97653i	−0.268347	−	0.194965i
$417$	−4.17454	−	16.4963i	−0.204428	−	0.807828i
$418$	0.815958	−	1.12307i	0.0399098	−	0.0549311i
$419$	11.8558	−	16.3181i	0.579193	−	0.797191i	−0.414413	−	0.910089i	$-0.636013\pi$
$419$	11.8558	−	16.3181i	0.579193	−	0.797191i	0.993607	+	0.112898i	$0.0360132\pi$
$420$	0.115757	+	0.457431i	0.00564836	+	0.0223204i
$421$	9.13913	+	6.63996i	0.445414	+	0.323612i	0.787782	−	0.615954i	$-0.211229\pi$
$421$	9.13913	+	6.63996i	0.445414	+	0.323612i	−0.342369	+	0.939566i	$0.611229\pi$
$422$	−4.30154	−	5.92057i	−0.209396	−	0.288209i
$423$	−33.7597	−	16.1734i	−1.64145	−	0.786377i
$424$	6.00482	+	8.26492i	0.291620	+	0.401380i
$425$	1.82647	+	5.62130i	0.0885969	+	0.272673i
$426$	7.35984	−	1.86247i	0.356586	−	0.0902371i
$427$	−2.72694	−	0.886037i	−0.131966	−	0.0428783i
$428$			2.06220i			0.0996802i
$429$	6.72264	+	0.446391i	0.324572	+	0.0215520i
$430$	2.05197	+	0.666726i	0.0989549	+	0.0321524i
$431$	−2.39496	+	3.29639i	−0.115361	+	0.158781i	−0.862793	−	0.505558i	$-0.831287\pi$
$431$	−2.39496	+	3.29639i	−0.115361	+	0.158781i	0.747432	+	0.664339i	$0.231287\pi$
$432$	−2.16332	−	4.72441i	−0.104083	−	0.227303i
$433$		−	15.7273i		−	0.755806i	−0.925845	−	0.377903i	$-0.876645\pi$
$433$		−	15.7273i		−	0.755806i	0.925845	−	0.377903i	$-0.123355\pi$
$434$	−0.223950	−	1.50016i	−0.0107499	−	0.0720102i
$435$	−4.21381	−	0.279802i	−0.202037	−	0.0134155i
$436$	3.65032	−	2.65211i	0.174818	−	0.127013i
$437$	10.3397	+	7.51225i	0.494616	+	0.359360i
$438$	−19.0526	−	7.62009i	−0.910370	−	0.364102i
$439$	−9.19440			−0.438825			−0.219413	−	0.975632i	$-0.570414\pi$
$439$	−9.19440			−0.438825			−0.219413	+	0.975632i	$0.570414\pi$
$440$	0.574975			0.0274109
$441$	8.97690	−	18.7380i	0.427471	−	0.892287i
$442$	−12.3566	−	38.0297i	−0.587743	−	1.80889i
$443$	−6.60622	+	2.14649i	−0.313871	+	0.101983i	−0.461716	−	0.887028i	$-0.652766\pi$
$443$	−6.60622	+	2.14649i	−0.313871	+	0.101983i	0.147845	+	0.989010i	$0.452766\pi$
$444$	14.4542	−	9.10270i	0.685968	−	0.431995i
$445$	14.4476	+	4.69430i	0.684880	+	0.222531i
$446$	−16.3648	+	11.8897i	−0.774896	+	0.562995i
$447$	7.13179	+	5.94176i	0.337322	+	0.281036i
$448$	−0.0841834	−	0.259090i	−0.00397729	−	0.0122408i
$449$	−7.96546	−	5.78725i	−0.375913	−	0.273117i	0.383745	−	0.923439i	$-0.374634\pi$
$449$	−7.96546	−	5.78725i	−0.375913	−	0.273117i	−0.759659	+	0.650322i	$0.774634\pi$
$450$	−2.06878	+	2.17259i	−0.0975231	+	0.102417i
$451$	−4.10178	+	1.33275i	−0.193145	+	0.0627566i
$452$	5.66014	−	7.79052i	0.266231	−	0.366435i
$453$	8.13179	−	5.12107i	0.382065	−	0.240609i
$454$	−0.948779	+	2.92004i	−0.0445284	+	0.137044i
$455$	−1.49103	+	1.08330i	−0.0699007	+	0.0507858i
$456$	−1.02590	−	4.05398i	−0.0480420	−	0.189845i
$457$	−1.52689	+	0.496118i	−0.0714250	+	0.0232074i	−0.344512	−	0.938782i	$-0.611955\pi$
$457$	−1.52689	+	0.496118i	−0.0714250	+	0.0232074i	0.273087	+	0.961989i	$0.411955\pi$
$458$	−8.41558	+	25.9005i	−0.393234	+	1.21025i
$459$	6.06883	−	30.1067i	0.283269	−	1.40526i
$460$			5.29360i			0.246816i
$461$	7.60371	−	23.4018i	0.354140	−	1.08993i	−0.602366	−	0.798220i	$-0.705775\pi$
$461$	7.60371	−	23.4018i	0.354140	−	1.08993i	0.956506	−	0.291712i	$-0.0942248\pi$
$462$	0.208440	+	0.173659i	0.00969753	+	0.00807937i
$463$	16.2602	+	22.3802i	0.755674	+	1.04010i	0.997562	+	0.0697916i	$0.0222334\pi$
$463$	16.2602	+	22.3802i	0.755674	+	1.04010i	−0.241888	+	0.970304i	$0.577767\pi$
$464$	2.43820			0.113191
$465$	7.31209	−	6.28755i	0.339090	−	0.291578i
$466$	−22.2597			−1.03116
$467$	−1.49867	−	2.06274i	−0.0693501	−	0.0954522i	0.772933	−	0.634488i	$-0.218789\pi$
$467$	−1.49867	−	2.06274i	−0.0693501	−	0.0954522i	−0.842283	+	0.539035i	$0.818789\pi$
$468$	13.9959	−	14.6982i	0.646959	−	0.679424i
$469$	0.821197	−	2.52738i	0.0379193	−	0.116704i
$470$		−	12.4780i		−	0.575565i
$471$	1.40776	−	21.2009i	0.0648664	−	0.976886i
$472$	3.93659	−	12.1156i	0.181196	−	0.557665i
$473$	1.17983	−	0.383351i	0.0542488	−	0.0176265i
$474$	9.65925	−	2.44436i	0.443664	−	0.112273i
$475$	−1.95325	+	1.41912i	−0.0896212	+	0.0651136i
$476$	0.497573	−	1.53137i	0.0228062	−	0.0701904i
$477$	−26.9589	+	14.5779i	−1.23437	+	0.667478i
$478$	−12.7578	+	17.5596i	−0.583526	+	0.803155i
$479$	−17.8946	+	5.81431i	−0.817625	+	0.265663i	−0.687824	−	0.725877i	$-0.741434\pi$
$479$	−17.8946	+	5.81431i	−0.817625	+	0.265663i	−0.129801	+	0.991540i	$0.541434\pi$
$480$	1.10868	−	1.33073i	0.0506040	−	0.0607391i
$481$	53.9776	+	39.2170i	2.46117	+	1.78814i
$482$	0.370152	+	1.13921i	0.0168600	+	0.0518896i
$483$	−1.59882	+	1.91904i	−0.0727490	+	0.0873194i
$484$	−8.63173	+	6.27132i	−0.392351	+	0.285060i
$485$	−2.73770	−	0.889534i	−0.124313	−	0.0403917i
$486$	14.9069	−	4.55902i	0.676190	−	0.206801i
$487$	−22.5834	+	7.33778i	−1.02335	+	0.332507i	−0.772158	−	0.635431i	$-0.780823\pi$
$487$	−22.5834	+	7.33778i	−1.02335	+	0.332507i	−0.251192	+	0.967937i	$0.580823\pi$
$488$	3.25243	+	10.0099i	0.147231	+	0.453129i
$489$	14.1104	+	5.64346i	0.638096	+	0.255206i
$490$	6.92579			0.312875
$491$	20.3125			0.916691			0.458345	−	0.888774i	$-0.348442\pi$
$491$	20.3125			0.916691			0.458345	+	0.888774i	$0.348442\pi$
$492$	−4.82460	+	12.0630i	−0.217510	+	0.543842i
$493$	11.6589	+	8.47069i	0.525091	+	0.381501i
$494$	13.2143	−	9.60073i	0.594538	−	0.431957i
$495$	−0.228069	+	1.70978i	−0.0102509	+	0.0768490i
$496$	−3.97185	+	3.90185i	−0.178341	+	0.175198i
$497$			1.19407i			0.0535615i
$498$	−14.2418	+	8.96894i	−0.638192	+	0.401908i
$499$	−9.68099	+	13.3247i	−0.433381	+	0.596497i	−0.968725	−	0.248136i	$-0.920182\pi$
$499$	−9.68099	+	13.3247i	−0.433381	+	0.596497i	0.535344	+	0.844634i	$0.320182\pi$
$500$	−0.951057	−	0.309017i	−0.0425325	−	0.0138197i
$501$	−0.329361	+	4.96016i	−0.0147147	+	0.221604i
$502$			19.5235i			0.871377i
$503$	−17.9498	−	5.83225i	−0.800343	−	0.260047i	−0.119840	−	0.992793i	$-0.538238\pi$
$503$	−17.9498	−	5.83225i	−0.800343	−	0.260047i	−0.680502	+	0.732746i	$0.738238\pi$
$504$	0.803837	−	0.147563i	0.0358058	−	0.00657297i
$505$	−3.74652	−	11.5306i	−0.166718	−	0.513105i
$506$	1.78904	+	2.46240i	0.0795324	+	0.109467i
$507$	52.6990	+	21.0770i	2.34044	+	0.936060i
$508$	12.0711	+	16.6145i	0.535570	+	0.737149i
$509$	34.9656	+	25.4040i	1.54982	+	1.12601i	0.943777	+	0.330584i	$0.107246\pi$
$509$	34.9656	+	25.4040i	1.54982	+	1.12601i	0.606047	+	0.795429i	$0.292754\pi$
$510$	9.92459	−	2.51150i	0.439468	−	0.111211i
$511$	1.89705	−	2.61106i	0.0839205	−	0.115507i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	12.4621	−	1.44262i	0.550215	−	0.0636933i
$514$	−10.9981	−	7.99057i	−0.485104	−	0.352449i
$515$	0.0865226	+	0.119088i	0.00381264	+	0.00524765i
$516$	1.38775	−	3.46980i	0.0610921	−	0.152749i
$517$	−4.21708	−	5.80431i	−0.185467	−	0.255273i
$518$	0.830227	+	2.55517i	0.0364781	+	0.112268i
$519$	−2.82695	−	11.1711i	−0.124089	−	0.490358i
$520$	6.43416	+	2.09059i	0.282157	+	0.0916783i
$521$			11.0722i			0.485080i	0.970141	+	0.242540i	$0.0779806\pi$
$521$			11.0722i			0.485080i	−0.970141	+	0.242540i	$0.922019\pi$
$522$	−0.967132	+	7.25039i	−0.0423302	+	0.317341i
$523$	−3.63433	−	1.18086i	−0.158918	−	0.0516356i	0.228478	−	0.973549i	$-0.426625\pi$
$523$	−3.63433	−	1.18086i	−0.158918	−	0.0516356i	−0.387396	+	0.921914i	$0.626625\pi$
$524$	8.61596	−	11.8588i	0.376390	−	0.518056i
$525$	−0.251445	−	0.399272i	−0.0109740	−	0.0174257i
$526$			30.2640i			1.31957i
$527$	−32.5481	+	4.85890i	−1.41782	+	0.211657i
$528$	0.0659827	−	0.993698i	0.00287153	−	0.0432452i
$529$	−4.06309	+	2.95200i	−0.176656	+	0.128348i
$530$	−8.26492	−	6.00482i	−0.359005	−	0.260833i
$531$	34.4662	+	16.5118i	1.49570	+	0.716553i
$532$	0.657724			0.0285159
$533$	−50.7460			−2.19805
$534$	9.77086	−	24.4302i	0.422827	−	1.05720i
$535$	−0.637255	−	1.96127i	−0.0275509	−	0.0847930i
$536$	−9.27742	+	3.01442i	−0.400723	+	0.130203i
$537$	6.92074	+	10.9895i	0.298652	+	0.474231i
$538$	−15.4778	−	5.02904i	−0.667296	−	0.216818i
$539$	3.22163	−	2.34065i	0.138765	−	0.100819i
$540$	3.51737	+	3.82468i	0.151363	+	0.164588i
$541$	−7.56557	−	23.2844i	−0.325269	−	1.00108i	−0.971319	−	0.237780i	$-0.923580\pi$
$541$	−7.56557	−	23.2844i	−0.325269	−	1.00108i	0.646050	−	0.763295i	$-0.276420\pi$
$542$	−2.91169	−	2.11546i	−0.125068	−	0.0908670i
$543$	28.7029	+	23.9134i	1.23176	+	1.02622i
$544$	−5.62130	+	1.82647i	−0.241011	+	0.0783093i
$545$	−2.65211	+	3.65032i	−0.113604	+	0.156362i
$546$	1.70110	+	2.70119i	0.0728003	+	0.115600i
$547$	2.30956	−	7.10808i	0.0987495	−	0.303920i	−0.889463	−	0.457007i	$-0.848922\pi$
$547$	2.30956	−	7.10808i	0.0987495	−	0.303920i	0.988213	+	0.153087i	$0.0489215\pi$
$548$	2.83623	−	2.06064i	0.121158	−	0.0880261i
$549$	−31.0563	+	5.70110i	−1.32545	+	0.243317i
$550$	−0.546834	+	0.177677i	−0.0233171	+	0.00757618i
$551$	−1.81908	+	5.59855i	−0.0774954	+	0.238506i
$552$	9.14865	+	0.607481i	0.389392	+	0.0258561i
$553$			1.56713i			0.0666412i
$554$	−5.88879	+	18.1238i	−0.250191	+	0.770008i
$555$	−10.9339	+	13.1238i	−0.464119	+	0.557074i
$556$	−5.77462	−	7.94809i	−0.244899	−	0.337074i
$557$	37.5044			1.58911			0.794557	−	0.607189i	$-0.207703\pi$
$557$	37.5044			1.58911			0.794557	+	0.607189i	$0.207703\pi$
$558$	−10.0273	−	13.3586i	−0.424490	−	0.565516i
$559$	14.5966			0.617369
$560$	0.160126	+	0.220395i	0.00676657	+	0.00931338i
$561$	3.76778	−	4.52240i	0.159076	−	0.190936i
$562$	0.124752	−	0.383946i	0.00526233	−	0.0161958i
$563$		−	5.63067i		−	0.237305i	−0.992936	−	0.118652i	$-0.962143\pi$
$563$		−	5.63067i		−	0.237305i	0.992936	−	0.118652i	$-0.0378574\pi$
$564$	−21.5650	−	1.43194i	−0.908049	−	0.0602955i
$565$	−2.97571	+	9.15830i	−0.125189	+	0.385293i
$566$	11.5964	−	3.76791i	0.487434	−	0.158377i
$567$	0.119953	+	2.44887i	0.00503757	+	0.102843i
$568$	3.54605	−	2.57635i	0.148789	−	0.108101i
$569$	8.57619	−	26.3948i	0.359533	−	1.10653i	−0.593802	−	0.804611i	$-0.702374\pi$
$569$	8.57619	−	26.3948i	0.359533	−	1.10653i	0.953334	−	0.301916i	$-0.0976264\pi$
$570$	2.22843	+	3.53855i	0.0933388	+	0.148213i
$571$	−2.07688	+	2.85858i	−0.0869148	+	0.119628i	−0.850260	−	0.526363i	$-0.823555\pi$
$571$	−2.07688	+	2.85858i	−0.0869148	+	0.119628i	0.763345	+	0.645991i	$0.223555\pi$
$572$	3.69948	−	1.20204i	0.154683	−	0.0502596i
$573$	8.44849	+	7.03875i	0.352941	+	0.294048i
$574$	−1.65317	−	1.20110i	−0.0690020	−	0.0501329i
$575$	−1.63581	−	5.03452i	−0.0682182	−	0.209954i
$576$	−2.17259	−	2.06878i	−0.0905247	−	0.0861991i
$577$	−2.86965	+	2.08492i	−0.119465	+	0.0867965i	−0.645914	−	0.763411i	$-0.723523\pi$
$577$	−2.86965	+	2.08492i	−0.119465	+	0.0867965i	0.526448	+	0.850207i	$0.323523\pi$
$578$	−17.0572	−	5.54224i	−0.709488	−	0.230527i
$579$	8.24320	+	13.0894i	0.342576	+	0.543978i
$580$	−2.31887	+	0.753446i	−0.0962857	+	0.0312851i
$581$	−0.818027	−	2.51763i	−0.0339375	−	0.104449i
$582$	−1.85150	+	4.62934i	−0.0767473	+	0.191892i
$583$	−5.87395			−0.243274
$584$	−11.8472			−0.490241
$585$	−8.76886	+	18.3038i	−0.362548	+	0.756768i
$586$	25.5621	+	18.5720i	1.05596	+	0.767201i
$587$	17.0600	−	12.3948i	0.704141	−	0.511588i	−0.177137	−	0.984186i	$-0.556684\pi$
$587$	17.0600	−	12.3948i	0.704141	−	0.511588i	0.881278	+	0.472598i	$0.156684\pi$
$588$	0.794786	−	11.9695i	0.0327764	−	0.493612i
$589$	−5.99605	−	12.0312i	−0.247063	−	0.495735i
$590$			12.7391i			0.524460i
$591$	10.0660	+	15.9838i	0.414059	+	0.657488i
$592$	5.79681	−	7.97862i	0.238247	−	0.327919i
$593$	1.11746	+	0.363083i	0.0458884	+	0.0149100i	0.331871	−	0.943325i	$-0.392320\pi$
$593$	1.11746	+	0.363083i	0.0458884	+	0.0149100i	−0.285983	+	0.958235i	$0.592320\pi$
$594$	2.92875	+	0.590369i	0.120168	+	0.0242231i
$595$			1.61018i			0.0660110i
$596$	5.09702	+	1.65612i	0.208782	+	0.0678374i
$597$	−5.63861	−	22.2818i	−0.230773	−	0.911935i
$598$	11.0667	+	34.0599i	0.452553	+	1.39281i
$599$	10.6296	+	14.6304i	0.434313	+	0.597781i	0.968937	−	0.247310i	$-0.0795465\pi$
$599$	10.6296	+	14.6304i	0.434313	+	0.597781i	−0.534623	+	0.845091i	$0.679546\pi$
$600$	−0.643198	+	1.60820i	−0.0262584	+	0.0656544i
$601$	6.85803	+	9.43927i	0.279745	+	0.385036i	0.925649	−	0.378382i	$-0.123520\pi$
$601$	6.85803	+	9.43927i	0.279745	+	0.385036i	−0.645904	+	0.763418i	$0.723520\pi$
$602$	0.475518	+	0.345484i	0.0193807	+	0.0140809i
$603$	−5.28389	−	28.7836i	−0.215177	−	1.17216i
$604$	3.26122	−	4.48868i	0.132697	−	0.182642i
$605$	6.27132	−	8.63173i	0.254965	−	0.350930i
$606$	−20.3577	+	5.15168i	−0.826973	+	0.209273i
$607$	24.9014	+	18.0919i	1.01071	+	0.734327i	0.964359	−	0.264598i	$-0.0852392\pi$
$607$	24.9014	+	18.0919i	1.01071	+	0.734327i	0.0463559	+	0.998925i	$0.485239\pi$
$608$	−1.41912	−	1.95325i	−0.0575528	−	0.0792147i
$609$	−1.06820	−	0.427226i	−0.0432857	−	0.0173121i
$610$	−6.18649	−	8.51497i	−0.250484	−	0.344761i
$611$	−26.0863	−	80.2852i	−1.05534	−	3.24799i
$612$	−3.20157	−	17.4403i	−0.129416	−	0.704984i
$613$	−3.50002	−	1.13722i	−0.141364	−	0.0459321i	0.237480	−	0.971392i	$-0.423679\pi$
$613$	−3.50002	−	1.13722i	−0.141364	−	0.0459321i	−0.378845	+	0.925460i	$0.623679\pi$
$614$		−	5.81380i		−	0.234626i
$615$	0.860790	−	12.9635i	0.0347104	−	0.522738i
$616$	0.148970	+	0.0484034i	0.00600218	+	0.00195023i
$617$	−5.33631	+	7.34480i	−0.214832	+	0.295691i	−0.902809	−	0.430042i	$-0.858499\pi$
$617$	−5.33631	+	7.34480i	−0.214832	+	0.295691i	0.687977	+	0.725732i	$0.258499\pi$
$618$	0.215743	−	0.135866i	0.00867844	−	0.00546533i
$619$			20.0124i			0.804366i	0.915559	+	0.402183i	$0.131749\pi$
$619$			20.0124i			0.804366i	−0.915559	+	0.402183i	$0.868251\pi$
$620$	2.57172	−	4.93825i	0.103283	−	0.198325i
$621$	−5.43533	+	26.9640i	−0.218112	+	1.08203i
$622$	−8.92434	+	6.48391i	−0.357833	+	0.259981i
$623$	3.34803	+	2.43249i	0.134136	+	0.0974556i
$624$	4.35141	−	10.8799i	0.174196	−	0.435545i
$625$	1.00000			0.0400000
$626$	−0.442003			−0.0176660
$627$	2.23248	+	0.892881i	0.0891568	+	0.0356582i
$628$	−3.79081	−	11.6669i	−0.151270	−	0.465560i
$629$	55.4380	−	18.0129i	2.21046	−	0.718221i
$630$	−0.718895	+	0.388740i	−0.0286415	+	0.0154878i
$631$	−22.7939	−	7.40618i	−0.907409	−	0.294835i	−0.182118	−	0.983277i	$-0.558295\pi$
$631$	−22.7939	−	7.40618i	−0.907409	−	0.294835i	−0.725292	+	0.688442i	$0.758295\pi$
$632$	4.65392	−	3.38127i	0.185123	−	0.134500i
$633$	8.11355	−	9.73856i	0.322485	−	0.387073i
$634$	−0.761611	−	2.34400i	−0.0302474	−	0.0930921i
$635$	−16.6145	−	12.0711i	−0.659326	−	0.479028i
$636$	−11.3263	+	13.5947i	−0.449115	+	0.539066i
$637$	44.5616	−	14.4790i	1.76560	−	0.573677i
$638$	−0.824019	+	1.13417i	−0.0326232	+	0.0449020i
$639$	6.25463	+	11.5667i	0.247430	+	0.457570i
$640$	0.309017	−	0.951057i	0.0122150	−	0.0375938i
$641$	17.7151	−	12.8707i	0.699703	−	0.508364i	−0.180133	−	0.983642i	$-0.557653\pi$
$641$	17.7151	−	12.8707i	0.699703	−	0.508364i	0.879835	+	0.475278i	$0.157653\pi$
$642$	−3.46268	+	0.876262i	−0.136661	+	0.0345833i
$643$	3.59837	−	1.16918i	0.141906	−	0.0461080i	−0.237203	−	0.971460i	$-0.576231\pi$
$643$	3.59837	−	1.16918i	0.141906	−	0.0461080i	0.379109	+	0.925352i	$0.376231\pi$
$644$	−0.445633	+	1.37152i	−0.0175604	+	0.0540454i
$645$	−0.247597	+	3.72881i	−0.00974914	+	0.146822i
$646$		−	14.2702i		−	0.561454i
$647$	3.65933	−	11.2623i	0.143863	−	0.442766i	−0.853000	−	0.521911i	$-0.825219\pi$
$647$	3.65933	−	11.2623i	0.143863	−	0.442766i	0.996863	+	0.0791456i	$0.0252192\pi$
$648$	7.01362	−	5.63996i	0.275521	−	0.221559i
$649$	4.30532	+	5.92577i	0.168999	+	0.232607i
$650$	−6.76528			−0.265356
$651$	2.42380	−	1.01348i	0.0949960	−	0.0397215i
$652$	8.77407			0.343619
$653$	24.7860	+	34.1149i	0.969950	+	1.33502i	0.942072	+	0.335410i	$0.108875\pi$
$653$	24.7860	+	34.1149i	0.969950	+	1.33502i	0.0278773	+	0.999611i	$0.491125\pi$
$654$	6.00429	+	5.00240i	0.234786	+	0.195609i
$655$	−4.52968	+	13.9409i	−0.176989	+	0.544716i
$656$			7.50095i			0.292863i
$657$	4.69929	−	35.2296i	0.183337	−	1.37444i
$658$	1.05044	−	3.23291i	0.0409503	−	0.126032i
$659$	−14.6108	+	4.74735i	−0.569158	+	0.184931i	−0.579438	−	0.815017i	$-0.696728\pi$
$659$	−14.6108	+	4.74735i	−0.569158	+	0.184931i	0.0102798	+	0.999947i	$0.496728\pi$
$660$	0.244316	+	0.965453i	0.00951000	+	0.0375802i
$661$	−5.49157	+	3.98986i	−0.213597	+	0.155187i	−0.689440	−	0.724343i	$-0.742143\pi$
$661$	−5.49157	+	3.98986i	−0.213597	+	0.155187i	0.475843	+	0.879530i	$0.342143\pi$
$662$	−9.55672	+	29.4126i	−0.371433	+	1.14315i
$663$	58.6059	−	36.9076i	2.27606	−	1.43337i
$664$	−5.71163	+	7.86138i	−0.221654	+	0.305081i
$665$	−0.625533	+	0.203248i	−0.0242571	+	0.00788161i
$666$	21.4264	+	20.4025i	0.830255	+	0.790582i
$667$	−10.4419	−	7.58647i	−0.404311	−	0.293749i
$668$	0.886897	+	2.72959i	0.0343151	+	0.105611i
$669$	−26.9179	−	22.4263i	−1.04071	−	0.867052i
$670$	7.89184	−	5.73376i	0.304889	−	0.221514i
$671$	−5.75547	−	1.87007i	−0.222188	−	0.0721931i
$672$	0.399272	−	0.251445i	0.0154023	−	0.00969972i
$673$	−8.03401	+	2.61041i	−0.309688	+	0.100624i	−0.459738	−	0.888055i	$-0.652057\pi$
$673$	−8.03401	+	2.61041i	−0.309688	+	0.100624i	0.150050	+	0.988678i	$0.452057\pi$
$674$	−0.121048	−	0.372547i	−0.00466259	−	0.0143500i
$675$	−4.52710	−	2.55056i	−0.174248	−	0.0981710i
$676$	32.7690			1.26035
$677$	6.74264			0.259141			0.129570	−	0.991570i	$-0.458640\pi$
$677$	6.74264			0.259141			0.129570	+	0.991570i	$0.458640\pi$
$678$	15.4863	+	6.19374i	0.594748	+	0.237869i
$679$	−0.634427	−	0.460938i	−0.0243471	−	0.0176892i
$680$	4.78177	−	3.47416i	0.183372	−	0.133228i
$681$	−5.30626	−	0.352341i	−0.203336	−	0.0135018i
$682$	−0.472668	−	3.16624i	−0.0180994	−	0.121242i
$683$		−	47.6805i		−	1.82444i	−0.409698	−	0.912221i	$-0.634366\pi$
$683$		−	47.6805i		−	1.82444i	0.409698	−	0.912221i	$-0.365634\pi$
$684$	6.37120	−	3.44520i	0.243609	−	0.131731i
$685$	−2.06064	+	2.83623i	−0.0787330	+	0.108367i
$686$	3.60803	+	1.17232i	0.137755	+	0.0447594i
$687$	−47.0660	−	3.12523i	−1.79568	−	0.119235i
$688$		−	2.15757i		−	0.0822566i
$689$	−65.7315	−	21.3574i	−2.50417	−	0.813654i
$690$	−8.88860	+	2.24934i	−0.338383	+	0.0856309i
$691$	2.02193	+	6.22285i	0.0769177	+	0.236728i	0.982121	−	0.188250i	$-0.0602816\pi$
$691$	2.02193	+	6.22285i	0.0769177	+	0.236728i	−0.905203	+	0.424979i	$0.860282\pi$
$692$	−3.91051	−	5.38236i	−0.148655	−	0.204606i
$693$	−0.203025	+	0.423787i	−0.00771230	+	0.0160984i
$694$	12.0363	+	16.5665i	0.456891	+	0.628856i
$695$	7.94809	+	5.77462i	0.301488	+	0.219044i
$696$	1.03603	+	4.09403i	0.0392707	+	0.155184i
$697$	−26.0595	+	35.8678i	−0.987073	+	1.35859i
$698$	12.1402	−	16.7096i	0.459515	−	0.632468i
$699$	−9.45849	−	37.3767i	−0.357753	−	1.41372i
$700$	−0.220395	−	0.160126i	−0.00833014	−	0.00605220i
$701$	−1.02376	−	1.40909i	−0.0386670	−	0.0532205i	0.789246	−	0.614077i	$-0.210472\pi$
$701$	−1.02376	−	1.40909i	−0.0386670	−	0.0532205i	−0.827913	+	0.560857i	$0.810472\pi$
$702$	30.6271	+	17.2552i	1.15595	+	0.651257i
$703$	13.9955	+	19.2632i	0.527851	+	0.726524i
$704$	−0.177677	−	0.546834i	−0.00669646	−	0.0206096i
$705$	20.9520	−	5.30209i	0.789098	−	0.199688i
$706$	−23.1646	−	7.52662i	−0.871810	−	0.283268i
$707$		−	3.30286i		−	0.124217i
$708$	22.0163	+	1.46190i	0.827421	+	0.0549417i
$709$	7.51338	+	2.44125i	0.282171	+	0.0916829i	0.446683	−	0.894692i	$-0.352605\pi$
$709$	7.51338	+	2.44125i	0.282171	+	0.0916829i	−0.164512	+	0.986375i	$0.552605\pi$
$710$	−2.57635	+	3.54605i	−0.0966888	+	0.133081i
$711$	8.20874	+	15.1804i	0.307852	+	0.569309i
$712$		−	15.1911i		−	0.569309i
$713$	29.1505	−	4.35170i	1.09170	−	0.162972i
$714$	2.78279	+	0.184780i	0.104143	+	0.00691523i
$715$	−3.14697	+	2.28641i	−0.117690	+	0.0855068i
$716$	6.06611	+	4.40728i	0.226701	+	0.164708i
$717$	−34.9056	−	13.9605i	−1.30357	−	0.521364i
$718$	−30.6851			−1.14516
$719$	2.84950			0.106268			0.0531341	−	0.998587i	$-0.483079\pi$
$719$	2.84950			0.106268			0.0531341	+	0.998587i	$0.483079\pi$
$720$	2.70555	+	1.29616i	0.100830	+	0.0483049i
$721$	0.0123919	+	0.0381383i	0.000461498	+	0.00142034i
$722$	−12.5263	+	4.07004i	−0.466180	+	0.151471i
$723$	−1.75559	+	1.10560i	−0.0652910	+	0.0411177i
$724$	20.5136	+	6.66529i	0.762384	+	0.247713i
$725$	1.97255	−	1.43314i	0.0732585	−	0.0532254i
$726$	−14.1981	−	11.8289i	−0.526939	−	0.439013i
$727$	−3.73632	−	11.4992i	−0.138573	−	0.426483i	0.857556	−	0.514391i	$-0.171982\pi$
$727$	−3.73632	−	11.4992i	−0.138573	−	0.426483i	−0.996129	+	0.0879081i	$0.971982\pi$
$728$	1.49103	+	1.08330i	0.0552614	+	0.0401497i
$729$	13.9893	+	23.0933i	0.518123	+	0.855306i
$730$	11.2674	−	3.66099i	0.417024	−	0.135499i
$731$	7.49574	−	10.3170i	0.277240	−	0.381588i
$732$	−15.4259	+	9.71461i	−0.570158	+	0.359062i
$733$	−5.32642	+	16.3930i	−0.196736	+	0.605491i	0.803216	+	0.595688i	$0.203120\pi$
$733$	−5.32642	+	16.3930i	−0.196736	+	0.605491i	−0.999952	+	0.00980314i	$0.996880\pi$
$734$	−25.2959	+	18.3785i	−0.933688	+	0.678364i
$735$	2.94288	+	11.6292i	0.108550	+	0.428951i
$736$	5.03452	−	1.63581i	0.185575	−	0.0602969i
$737$	1.73321	−	5.33429i	0.0638438	−	0.196491i
$738$	−22.3053	−	2.97531i	−0.821069	−	0.109523i
$739$			26.3577i			0.969582i	0.874630	+	0.484791i	$0.161104\pi$
$739$			26.3577i			0.969582i	−0.874630	+	0.484791i	$0.838896\pi$
$740$	−3.04756	+	9.37944i	−0.112031	+	0.344795i
$741$	21.7357	+	18.1088i	0.798482	+	0.665245i
$742$	−1.63585	−	2.25156i	−0.0600540	−	0.0826572i
$743$	33.2316			1.21915			0.609575	−	0.792729i	$-0.291340\pi$
$743$	33.2316			1.21915			0.609575	+	0.792729i	$0.291340\pi$
$744$	−8.23938	−	5.01125i	−0.302070	−	0.183722i
$745$	−5.35932			−0.196350
$746$	−5.98864	−	8.24266i	−0.219260	−	0.301785i
$747$	−21.1115	−	20.1027i	−0.772430	−	0.735520i
$748$	1.05018	−	3.23211i	0.0383982	−	0.118178i
$749$		−	0.561791i		−	0.0205274i
$750$	0.114757	−	1.72824i	0.00419035	−	0.0631066i
$751$	5.30118	−	16.3153i	0.193443	−	0.595355i	−0.806549	−	0.591168i	$-0.798667\pi$
$751$	5.30118	−	16.3153i	0.193443	−	0.595355i	0.999991	−	0.00418756i	$-0.00133294\pi$
$752$	−11.8672	+	3.85590i	−0.432754	+	0.140610i
$753$	−32.7823	+	8.29585i	−1.19465	+	0.302318i
$754$	−13.3448	+	9.69558i	−0.485990	+	0.353092i
$755$	−1.71452	+	5.27676i	−0.0623979	+	0.192041i
$756$	0.589339	+	1.28704i	0.0214341	+	0.0468091i
$757$	−8.11950	+	11.1755i	−0.295108	+	0.406182i	−0.930665	−	0.365873i	$-0.880771\pi$
$757$	−8.11950	+	11.1755i	−0.295108	+	0.406182i	0.635557	+	0.772054i	$0.280771\pi$
$758$	31.5742	−	10.2591i	1.14683	−	0.372627i
$759$	−3.37447	+	4.05032i	−0.122486	+	0.147017i
$760$	1.95325	+	1.41912i	0.0708518	+	0.0514768i
$761$	−8.81869	−	27.1411i	−0.319677	−	0.983865i	−0.973786	−	0.227465i	$-0.926956\pi$
$761$	−8.81869	−	27.1411i	−0.319677	−	0.983865i	0.654109	−	0.756400i	$-0.273044\pi$
$762$	−22.7685	+	27.3287i	−0.824816	+	0.990013i
$763$	−0.994430	+	0.722496i	−0.0360008	+	0.0261561i
$764$	6.03805	+	1.96188i	0.218449	+	0.0709783i
$765$	8.43424	+	15.5974i	0.304941	+	0.563925i
$766$	−20.2387	+	6.57595i	−0.731254	+	0.237599i
$767$	26.6321	+	81.9653i	0.961631	+	2.95960i
$768$	−1.60820	−	0.643198i	−0.0580308	−	0.0232094i
$769$	−10.5150			−0.379182			−0.189591	−	0.981863i	$-0.560716\pi$
$769$	−10.5150			−0.379182			−0.189591	+	0.981863i	$0.560716\pi$
$770$	−0.156637			−0.00564479
$771$	8.74387	−	21.8624i	0.314903	−	0.787356i
$772$	7.22526	+	5.24946i	0.260043	+	0.188932i
$773$	16.3826	−	11.9026i	0.589240	−	0.428108i	−0.252803	−	0.967518i	$-0.581353\pi$
$773$	16.3826	−	11.9026i	0.589240	−	0.428108i	0.842044	+	0.539410i	$0.181353\pi$
$774$	6.41589	+	0.855818i	0.230614	+	0.0307617i
$775$	−0.919844	+	5.49126i	−0.0330418	+	0.197252i
$776$			2.87859i			0.103335i
$777$	−3.93767	+	2.47979i	−0.141263	+	0.0889618i
$778$	0.939071	−	1.29252i	0.0336673	−	0.0463391i
$779$	−17.2235	−	5.59627i	−0.617097	−	0.200507i
$780$	−0.776366	+	11.6921i	−0.0277984	+	0.418643i
$781$			2.52021i			0.0901800i
$782$	29.7570	+	9.66862i	1.06411	+	0.345749i
$783$	−12.5852	+	1.45688i	−0.449759	+	0.0520645i
$784$	−2.14019	−	6.58681i	−0.0764352	−	0.235243i
$785$	7.21054	+	9.92446i	0.257355	+	0.354219i
$786$	23.5735	+	9.42821i	0.840839	+	0.336293i
$787$	11.1098	+	15.2913i	0.396021	+	0.545077i	0.959740	−	0.280890i	$-0.0906297\pi$
$787$	11.1098	+	15.2913i	0.396021	+	0.545077i	−0.563718	+	0.825967i	$0.690630\pi$
$788$	8.82295	+	6.41025i	0.314305	+	0.228356i
$789$	−50.8169	+	12.8597i	−1.80913	+	0.457816i
$790$	−3.38127	+	4.65392i	−0.120300	+	0.165579i
$791$	−1.54195	+	2.12232i	−0.0548255	+	0.0754609i
$792$	1.69658	−	0.311446i	0.0602852	−	0.0110667i
$793$	−57.6061	−	41.8533i	−2.04565	−	1.48625i
$794$	−8.17217	−	11.2480i	−0.290019	−	0.399177i
$795$	6.57091	−	16.4293i	0.233046	−	0.582689i
$796$	−7.79987	−	10.7356i	−0.276459	−	0.380513i
$797$	−2.86628	−	8.82151i	−0.101529	−	0.312474i	0.887371	−	0.461056i	$-0.152529\pi$
$797$	−2.86628	−	8.82151i	−0.101529	−	0.312474i	−0.988900	+	0.148582i	$0.952529\pi$
$798$	0.279478	+	1.10440i	0.00989340	+	0.0390953i
$799$	−70.1424	−	22.7906i	−2.48146	−	0.806275i
$800$			1.00000i			0.0353553i
$801$	45.1731	+	6.02566i	1.59611	+	0.212906i
$802$	−32.2308	−	10.4724i	−1.13811	−	0.369794i
$803$	4.00390	−	5.51090i	0.141295	−	0.194475i
$804$	−9.00369	−	14.2970i	−0.317536	−	0.504217i
$805$		−	1.44210i		−	0.0508274i
$806$	6.22300	−	37.1499i	0.219196	−	1.30855i
$807$	1.86760	−	28.1260i	0.0657427	−	0.990083i
$808$	−9.80852	+	7.12631i	−0.345063	+	0.250703i
$809$	−17.0191	−	12.3651i	−0.598359	−	0.434733i	0.246937	−	0.969032i	$-0.420576\pi$
$809$	−17.0191	−	12.3651i	−0.598359	−	0.434733i	−0.845296	+	0.534298i	$0.820576\pi$
$810$	−4.92751	+	7.53125i	−0.173135	+	0.264621i
$811$	−29.7279			−1.04389			−0.521943	−	0.852980i	$-0.674793\pi$
$811$	−29.7279			−1.04389			−0.521943	+	0.852980i	$0.674793\pi$
$812$	−0.664222			−0.0233096
$813$	2.31490	−	5.78797i	0.0811870	−	0.202993i
$814$	1.75227	+	5.39294i	0.0614172	+	0.189023i
$815$	−8.34464	+	2.71134i	−0.292300	+	0.0949740i
$816$	−5.45545	−	8.66275i	−0.190979	−	0.303257i
$817$	4.95417	+	1.60971i	0.173325	+	0.0563166i
$818$	−1.88803	+	1.37173i	−0.0660134	+	0.0479616i
$819$	−3.81279	+	4.00413i	−0.133230	+	0.139916i
$820$	−2.31792	−	7.13383i	−0.0809453	−	0.249124i
$821$	16.0714	+	11.6766i	0.560897	+	0.407515i	0.831787	−	0.555095i	$-0.187318\pi$
$821$	16.0714	+	11.6766i	0.560897	+	0.407515i	−0.270890	+	0.962610i	$0.587318\pi$
$822$	4.66522	+	3.88677i	0.162718	+	0.135567i
$823$	−0.0423440	+	0.0137584i	−0.00147602	+	0.000479587i	−0.309755	−	0.950816i	$-0.600247\pi$
$823$	−0.0423440	+	0.0137584i	−0.00147602	+	0.000479587i	0.308279	+	0.951296i	$0.400247\pi$
$824$	0.0865226	−	0.119088i	0.00301416	−	0.00414863i
$825$	−0.530700	−	0.842702i	−0.0184766	−	0.0293391i
$826$	−1.07242	+	3.30057i	−0.0373142	+	0.114841i
$827$	−19.7735	+	14.3663i	−0.687591	+	0.499564i	−0.875867	−	0.482552i	$-0.839710\pi$
$827$	−19.7735	+	14.3663i	−0.687591	+	0.499564i	0.188277	+	0.982116i	$0.439710\pi$
$828$	2.86737	+	15.6198i	0.0996482	+	0.542826i
$829$	10.4128	−	3.38334i	0.361653	−	0.117508i	−0.122554	−	0.992462i	$-0.539108\pi$
$829$	10.4128	−	3.38334i	0.361653	−	0.117508i	0.484206	+	0.874954i	$0.339108\pi$
$830$	3.00278	−	9.24161i	0.104228	−	0.320781i
$831$	−32.9343	−	2.18688i	−1.14248	−	0.0758620i
$832$		−	6.76528i		−	0.234544i
$833$	12.6498	−	38.9319i	0.438288	−	1.34891i
$834$	10.8921	−	13.0736i	0.377161	−	0.452700i
$835$	−1.68698	−	2.32193i	−0.0583803	−	0.0803535i
$836$	1.38819			0.0480116
$837$	18.1700	−	22.5134i	0.628047	−	0.778176i
$838$	20.1703			0.696771
$839$	−3.03160	−	4.17264i	−0.104663	−	0.144056i	0.753473	−	0.657479i	$-0.228377\pi$
$839$	−3.03160	−	4.17264i	−0.104663	−	0.144056i	−0.858136	+	0.513423i	$0.828377\pi$
$840$	−0.302029	+	0.362521i	−0.0104210	+	0.0125082i
$841$	−7.12444	+	21.9268i	−0.245670	+	0.756096i
$842$			11.2966i			0.389306i
$843$	0.697700	+	0.0463281i	0.0240301	+	0.00159562i
$844$	2.26146	−	6.96005i	0.0778425	−	0.239575i
$845$	−31.1652	+	10.1262i	−1.07211	+	0.348351i
$846$	−6.75891	−	36.8186i	−0.232376	−	1.26585i
$847$	2.35148	−	1.70845i	0.0807979	−	0.0587031i
$848$	−3.15692	+	9.71600i	−0.108409	+	0.333649i
$849$	11.2543	+	17.8708i	0.386246	+	0.613323i
$850$	−3.47416	+	4.78177i	−0.119163	+	0.164013i
$851$	−49.6510	+	16.1326i	−1.70202	+	0.553018i
$852$	5.83278	+	4.85950i	0.199828	+	0.166484i
$853$	−31.8862	−	23.1667i	−1.09176	−	0.793212i	−0.112067	−	0.993701i	$-0.535747\pi$
$853$	−31.8862	−	23.1667i	−1.09176	−	0.793212i	−0.979696	+	0.200489i	$0.935747\pi$
$854$	−0.886037	−	2.72694i	−0.0303196	−	0.0933140i
$855$	−4.99475	+	5.24539i	−0.170817	+	0.179389i
$856$	−1.66835	+	1.21213i	−0.0570232	+	0.0414298i
$857$	9.16016	+	2.97632i	0.312905	+	0.101669i	0.461260	−	0.887265i	$-0.347398\pi$
$857$	9.16016	+	2.97632i	0.312905	+	0.101669i	−0.148354	+	0.988934i	$0.547398\pi$
$858$	3.59033	+	5.70112i	0.122572	+	0.194633i
$859$	−26.4938	+	8.60837i	−0.903958	+	0.293714i	−0.723870	−	0.689937i	$-0.757638\pi$
$859$	−26.4938	+	8.60837i	−0.903958	+	0.293714i	−0.180088	+	0.983650i	$0.557638\pi$
$860$	0.666726	+	2.05197i	0.0227352	+	0.0699717i
$861$	1.31433	−	3.28624i	0.0447923	−	0.111995i
$862$	−4.07456			−0.138780
$863$	6.83641			0.232714			0.116357	−	0.993207i	$-0.462878\pi$
$863$	6.83641			0.232714			0.116357	+	0.993207i	$0.462878\pi$
$864$	2.55056	−	4.52710i	0.0867717	−	0.154015i
$865$	5.38236	+	3.91051i	0.183006	+	0.132961i
$866$	12.7237	−	9.24428i	0.432368	−	0.314133i
$867$	2.05818	−	30.9962i	0.0698995	−	1.05268i
$868$	1.08202	−	1.06295i	0.0367263	−	0.0360790i
$869$			3.30758i			0.112202i
$870$	−2.25045	−	3.57351i	−0.0762974	−	0.121153i
$871$	38.7905	−	53.3905i	1.31437	−	1.80907i
$872$	4.29120	+	1.39430i	0.145318	+	0.0472168i
$873$	−8.55996	−	1.14182i	−0.289711	−	0.0386446i
$874$			12.7806i			0.432310i
$875$	0.259090	+	0.0841834i	0.00875883	+	0.00284592i
$876$	−5.03407	−	19.8929i	−0.170085	−	0.672118i
$877$	−8.81729	−	27.1368i	−0.297739	−	0.916346i	−0.982288	−	0.187379i	$-0.940001\pi$
$877$	−8.81729	−	27.1368i	−0.297739	−	0.916346i	0.684549	−	0.728967i	$-0.259999\pi$
$878$	−5.40434	−	7.43843i	−0.182387	−	0.251035i
$879$	−20.3228	+	50.8134i	−0.685472	+	1.71389i
$880$	0.337962	+	0.465165i	0.0113927	+	0.0156807i
$881$	−14.1432	−	10.2756i	−0.476496	−	0.346195i	0.323471	−	0.946238i	$-0.395150\pi$
$881$	−14.1432	−	10.2756i	−0.476496	−	0.346195i	−0.799968	+	0.600043i	$0.795150\pi$
$882$	20.4359	−	3.75147i	0.688112	−	0.126319i
$883$	−19.7215	+	27.1443i	−0.663682	+	0.913480i	−0.999596	−	0.0284129i	$-0.990955\pi$
$883$	−19.7215	+	27.1443i	−0.663682	+	0.913480i	0.335915	+	0.941892i	$0.390955\pi$
$884$	23.5036	−	32.3500i	0.790513	−	1.08805i
$885$	−21.3905	+	5.41304i	−0.719032	+	0.181957i
$886$	−5.61958	−	4.08287i	−0.188794	−	0.137167i
$887$	16.9048	+	23.2675i	0.567609	+	0.781247i	0.992269	−	0.124106i	$-0.0396063\pi$
$887$	16.9048	+	23.2675i	0.567609	+	0.781247i	−0.424660	+	0.905353i	$0.639606\pi$
$888$	15.8602	+	6.34330i	0.532235	+	0.212867i
$889$	−3.28846	−	4.52617i	−0.110291	−	0.151803i
$890$	4.69430	+	14.4476i	0.157353	+	0.484284i
$891$	0.253173	+	5.16858i	0.00848162	+	0.173154i
$892$	−19.2380	−	6.25080i	−0.644135	−	0.209292i
$893$		−	30.1261i		−	1.00813i
$894$	−0.615022	+	9.26222i	−0.0205694	+	0.309775i
$895$	−7.13114	−	2.31705i	−0.238368	−	0.0774503i
$896$	0.160126	−	0.220395i	0.00534944	−	0.00736288i
$897$	−52.4883	+	33.0550i	−1.75253	+	1.10367i
$898$		−	9.84585i		−	0.328560i
$899$	6.05530	+	12.1500i	0.201955	+	0.405226i
$900$	−2.97366	−	0.396658i	−0.0991220	−	0.0132219i
$901$	−48.8506	+	35.4920i	−1.62745	+	1.18241i
$902$	−3.48918	−	2.53504i	−0.116177	−	0.0844075i
$903$	−0.378054	+	0.945253i	−0.0125808	+	0.0314561i
$904$	9.62961			0.320276
$905$	−21.5693			−0.716988
$906$	8.92278	+	3.56866i	0.296440	+	0.118561i
$907$	−2.20593	−	6.78916i	−0.0732468	−	0.225430i	0.907730	−	0.419554i	$-0.137814\pi$
$907$	−2.20593	−	6.78916i	−0.0732468	−	0.225430i	−0.980977	+	0.194124i	$0.937814\pi$
$908$	−2.92004	+	0.948779i	−0.0969050	+	0.0314863i
$909$	−17.3006	−	31.9939i	−0.573825	−	1.06117i
$910$	−1.75281	−	0.569524i	−0.0581052	−	0.0188795i
$911$	−33.3882	+	24.2579i	−1.10620	+	0.803702i	−0.982061	−	0.188563i	$-0.939617\pi$
$911$	−33.3882	+	24.2579i	−1.10620	+	0.803702i	−0.124139	+	0.992265i	$0.539617\pi$
$912$	2.67673	−	3.21284i	0.0886355	−	0.106388i
$913$	−1.72652	−	5.31370i	−0.0571396	−	0.175858i
$914$	−1.29885	−	0.943672i	−0.0429622	−	0.0312139i
$915$	11.6689	−	14.0060i	0.385763	−	0.463024i
$916$	−25.9005	+	8.41558i	−0.855776	+	0.278059i
$917$	−2.34719	+	3.23062i	−0.0775109	+	0.106685i
$918$	27.9240	−	12.7865i	0.921630	−	0.422018i
$919$	−2.27348	+	6.99706i	−0.0749953	+	0.230812i	−0.981526	−	0.191328i	$-0.938721\pi$
$919$	−2.27348	+	6.99706i	−0.0749953	+	0.230812i	0.906531	+	0.422139i	$0.138721\pi$
$920$	−4.28262	+	3.11150i	−0.141194	+	0.102583i
$921$	9.76206	−	2.47038i	0.321671	−	0.0814017i
$922$	23.4018	−	7.60371i	0.770698	−	0.250415i
$923$	−9.16336	+	28.2019i	−0.301616	+	0.928278i
$924$	−0.0179752	+	0.270706i	−0.000591341	+	0.00890558i
$925$		−	9.86212i		−	0.324265i
$926$	−8.54847	+	26.3095i	−0.280920	+	0.864584i
$927$	0.319808	+	0.304526i	0.0105039	+	0.0100019i
$928$	1.43314	+	1.97255i	0.0470451	+	0.0647520i
$929$	49.3429			1.61889			0.809444	−	0.587197i	$-0.199769\pi$
$929$	49.3429			1.61889			0.809444	+	0.587197i	$0.199769\pi$
$930$	9.38468	+	2.21988i	0.307736	+	0.0727927i
$931$	16.7213			0.548017
$932$	−13.0839	−	18.0084i	−0.428578	−	0.589886i
$933$	−14.6794	−	12.2299i	−0.480581	−	0.400390i
$934$	0.787896	−	2.42490i	0.0257808	−	0.0793450i
$935$			3.39844i			0.111141i
$936$	20.1176	+	2.68350i	0.657566	+	0.0877130i
$937$	3.23354	−	9.95182i	0.105635	−	0.325112i	−0.884244	−	0.467026i	$-0.845326\pi$
$937$	3.23354	−	9.95182i	0.105635	−	0.325112i	0.989879	+	0.141914i	$0.0453256\pi$
$938$	2.52738	−	0.821197i	0.0825220	−	0.0268130i
$939$	−0.187814	−	0.742176i	−0.00612909	−	0.0242200i
$940$	10.0949	−	7.33436i	0.329259	−	0.239220i
$941$	12.2349	−	37.6553i	0.398847	−	1.22753i	−0.527077	−	0.849818i	$-0.676712\pi$
$941$	12.2349	−	37.6553i	0.398847	−	1.22753i	0.925924	−	0.377709i	$-0.123288\pi$
$942$	17.9794	−	11.3227i	0.585799	−	0.368913i
$943$	23.3392	−	32.1237i	0.760030	−	1.04609i
$944$	12.1156	−	3.93659i	0.394329	−	0.128125i
$945$	−0.958212	−	1.04193i	−0.0311706	−	0.0338940i
$946$	1.00363	+	0.729177i	0.0326307	+	0.0237076i
$947$	17.0527	+	52.4827i	0.554137	+	1.70546i	0.698211	+	0.715892i	$0.253980\pi$
$947$	17.0527	+	52.4827i	0.554137	+	1.70546i	−0.144074	+	0.989567i	$0.546020\pi$
$948$	7.65509	+	6.37774i	0.248626	+	0.207139i
$949$	64.8424	−	47.1108i	2.10487	−	1.52928i
$950$	−2.29618	−	0.746074i	−0.0744979	−	0.0242058i
$951$	3.61224	−	2.27484i	0.117135	−	0.0737667i
$952$	1.53137	−	0.497573i	0.0496321	−	0.0161264i
$953$	5.76782	+	17.7515i	0.186838	+	0.575028i	0.999975	−	0.00704391i	$-0.00224217\pi$
$953$	5.76782	+	17.7515i	0.186838	+	0.575028i	−0.813137	+	0.582072i	$0.802242\pi$
$954$	−27.6399	−	13.2415i	−0.894874	−	0.428711i
$955$	−6.34878			−0.205442
$956$	−21.7048			−0.701983
$957$	−2.25454	−	0.901703i	−0.0728789	−	0.0291479i
$958$	−15.2221	−	11.0595i	−0.491803	−	0.357315i
$959$	−0.772653	+	0.561366i	−0.0249503	+	0.0181274i
$960$	1.72824	+	0.114757i	0.0557789	+	0.00370378i
$961$	−29.3078	−	10.1022i	−0.945412	−	0.325877i
$962$			66.7200i			2.15114i
$963$	−2.94270	−	5.44192i	−0.0948271	−	0.175363i
$964$	−0.704071	+	0.969070i	−0.0226766	+	0.0312116i
$965$	−8.49380	−	2.75980i	−0.273425	−	0.0888412i
$966$	−2.49230	−	0.165492i	−0.0801885	−	0.00532461i
$967$			50.4717i			1.62306i	0.584311	+	0.811530i	$0.301365\pi$
$967$			50.4717i			1.62306i	−0.584311	+	0.811530i	$0.698635\pi$
$968$	−10.1472	−	3.29703i	−0.326144	−	0.105970i
$969$	23.9614	−	6.06364i	0.769751	−	0.194792i
$970$	−0.889534	−	2.73770i	−0.0285612	−	0.0879024i
$971$	−2.82800	−	3.89240i	−0.0907547	−	0.124913i	0.761225	−	0.648488i	$-0.224598\pi$
$971$	−2.82800	−	3.89240i	−0.0907547	−	0.124913i	−0.851980	+	0.523574i	$0.824598\pi$
$972$	12.4504	+	9.38020i	0.399346	+	0.300870i
$973$	1.57314	+	2.16524i	0.0504326	+	0.0694145i
$974$	−19.2106	−	13.9573i	−0.615546	−	0.447220i
$975$	−2.87468	−	11.3597i	−0.0920633	−	0.363802i
$976$	−6.18649	+	8.51497i	−0.198025	+	0.272558i
$977$	−4.46834	+	6.15014i	−0.142955	+	0.196761i	−0.874490	−	0.485043i	$-0.838804\pi$
$977$	−4.46834	+	6.15014i	−0.142955	+	0.196761i	0.731536	+	0.681803i	$0.238804\pi$
$978$	3.72825	+	14.7327i	0.119216	+	0.471101i
$979$	7.06635	+	5.13400i	0.225842	+	0.164083i
$980$	4.07087	+	5.60308i	0.130039	+	0.178984i
$981$	−5.84831	+	12.2075i	−0.186722	+	0.389756i
$982$	11.9394	+	16.4332i	0.381001	+	0.524403i
$983$	−2.89303	−	8.90383i	−0.0922733	−	0.283988i	0.894260	−	0.447547i	$-0.147702\pi$
$983$	−2.89303	−	8.90383i	−0.0922733	−	0.283988i	−0.986533	+	0.163559i	$0.947702\pi$
$984$	−12.5950	+	3.18728i	−0.401514	+	0.101607i
$985$	−10.3720	−	3.37007i	−0.330479	−	0.107379i
$986$			14.4112i			0.458946i
$987$	5.87480	+	0.390093i	0.186997	+	0.0124168i
$988$	15.5343	+	5.04740i	0.494212	+	0.160579i
$989$	−6.71329	+	9.24005i	−0.213470	+	0.293816i
$990$	−1.51730	+	0.820473i	−0.0482229	+	0.0260763i
$991$		−	45.4947i		−	1.44519i	−0.691273	−	0.722594i	$-0.742950\pi$
$991$		−	45.4947i		−	1.44519i	0.691273	−	0.722594i	$-0.257050\pi$
$992$	−5.49126	−	0.919844i	−0.174348	−	0.0292051i
$993$	−53.4480	−	3.54901i	−1.69612	−	0.112624i
$994$	−0.966025	+	0.701858i	−0.0306404	+	0.0222616i
$995$	10.7356	+	7.79987i	0.340342	+	0.247273i
$996$	−15.6272	−	6.25008i	−0.495166	−	0.198042i
$997$	−49.1597			−1.55690			−0.778452	−	0.627704i	$-0.783995\pi$
$997$	−49.1597			−1.55690			−0.778452	+	0.627704i	$0.783995\pi$
$998$	−16.4703			−0.521358
$999$	−25.1539	+	44.6468i	−0.795834	+	1.41256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.v.a.821.13	yes	80
3.2	odd	2	inner	930.2.v.a.821.4	yes	80
31.29	odd	10	inner	930.2.v.a.401.4	✓	80
93.29	even	10	inner	930.2.v.a.401.13	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.v.a.401.4	✓	80	31.29	odd	10	inner
930.2.v.a.401.13	yes	80	93.29	even	10	inner
930.2.v.a.821.4	yes	80	3.2	odd	2	inner
930.2.v.a.821.13	yes	80	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.v (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(-1.10868 + 1.33073i) q^{3} +(-0.309017 + 0.951057i) q^{4} -1.00000i q^{5} +(-1.72824 - 0.114757i) q^{6} +(0.0841834 - 0.259090i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.541668 - 2.95069i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(-1.10868 + 1.33073i) q^{3} +(-0.309017 + 0.951057i) q^{4} -1.00000i q^{5} +(-1.72824 - 0.114757i) q^{6} +(0.0841834 - 0.259090i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.541668 - 2.95069i) q^{9} +(0.809017 - 0.587785i) q^{10} +(0.177677 - 0.546834i) q^{11} +(-0.922996 - 1.46563i) q^{12} +(3.97653 - 5.47323i) q^{13} +(0.259090 - 0.0841834i) q^{14} +(1.33073 + 1.10868i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.82647 - 5.62130i) q^{17} +(2.06878 - 2.17259i) q^{18} +(1.95325 - 1.41912i) q^{19} +(0.951057 + 0.309017i) q^{20} +(0.251445 + 0.399272i) q^{21} +(0.546834 - 0.177677i) q^{22} +(1.63581 + 5.03452i) q^{23} +(0.643198 - 1.60820i) q^{24} -1.00000 q^{25} +6.76528 q^{26} +(4.52710 + 2.55056i) q^{27} +(0.220395 + 0.160126i) q^{28} +(-1.97255 + 1.43314i) q^{29} +(-0.114757 + 1.72824i) q^{30} +(0.919844 - 5.49126i) q^{31} -1.00000i q^{32} +(0.530700 + 0.842702i) q^{33} +(3.47416 - 4.78177i) q^{34} +(-0.259090 - 0.0841834i) q^{35} +(2.97366 + 0.396658i) q^{36} +9.86212i q^{37} +(2.29618 + 0.746074i) q^{38} +(2.87468 + 11.3597i) q^{39} +(0.309017 + 0.951057i) q^{40} +(-4.40895 - 6.06840i) q^{41} +(-0.175222 + 0.438110i) q^{42} +(1.26819 + 1.74551i) q^{43} +(0.465165 + 0.337962i) q^{44} +(-2.95069 + 0.541668i) q^{45} +(-3.11150 + 4.28262i) q^{46} +(7.33436 - 10.0949i) q^{47} +(1.67912 - 0.424916i) q^{48} +(5.60308 + 4.07087i) q^{49} +(-0.587785 - 0.809017i) q^{50} +(9.50539 + 3.80168i) q^{51} +(3.97653 + 5.47323i) q^{52} +(-3.15692 - 9.71600i) q^{53} +(0.597520 + 5.16168i) q^{54} +(-0.546834 - 0.177677i) q^{55} +0.272423i q^{56} +(-0.277064 + 4.17258i) q^{57} +(-2.31887 - 0.753446i) q^{58} +(-7.48784 + 10.3061i) q^{59} +(-1.46563 + 0.922996i) q^{60} -10.5251i q^{61} +(4.98319 - 2.48351i) q^{62} +(-0.810094 - 0.108059i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-5.47323 - 3.97653i) q^{65} +(-0.369823 + 0.924673i) q^{66} +9.75486 q^{67} +5.91059 q^{68} +(-8.51316 - 3.40484i) q^{69} +(-0.0841834 - 0.259090i) q^{70} +(-4.16863 + 1.35447i) q^{71} +(1.42697 + 2.63889i) q^{72} +(11.2674 + 3.66099i) q^{73} +(-7.97862 + 5.79681i) q^{74} +(1.10868 - 1.33073i) q^{75} +(0.746074 + 2.29618i) q^{76} +(-0.126722 - 0.0920686i) q^{77} +(-7.50051 + 9.00274i) q^{78} +(-5.47101 + 1.77764i) q^{79} +(-0.587785 + 0.809017i) q^{80} +(-8.41319 + 3.19659i) q^{81} +(2.31792 - 7.13383i) q^{82} +(7.86138 - 5.71163i) q^{83} +(-0.457431 + 0.115757i) q^{84} +(-5.62130 + 1.82647i) q^{85} +(-0.666726 + 2.05197i) q^{86} +(0.279802 - 4.21381i) q^{87} +0.574975i q^{88} +(-4.69430 + 14.4476i) q^{89} +(-2.17259 - 2.06878i) q^{90} +(-1.08330 - 1.49103i) q^{91} -5.29360 q^{92} +(6.28755 + 7.31209i) q^{93} +12.4780 q^{94} +(-1.41912 - 1.95325i) q^{95} +(1.33073 + 1.10868i) q^{96} +(0.889534 - 2.73770i) q^{97} +6.92579i q^{98} +(-1.70978 - 0.228069i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9}+O(q^{10}) \) 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9	\( 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9} + 20 q^{10} - 10 q^{13} - 20 q^{16} - 12 q^{18} - 12 q^{19} + 30 q^{21} + 10 q^{22} - 80 q^{25} + 18 q^{28} + 16 q^{31} + 72 q^{33} + 10 q^{34} + 8 q^{36} + 54 q^{39} - 20 q^{40} + 50 q^{43} + 8 q^{45} - 10 q^{46} + 8 q^{49} - 44 q^{51} - 10 q^{52} - 10 q^{55} + 30 q^{58} + 28 q^{63} + 20 q^{64} + 66 q^{66} + 60 q^{67} + 20 q^{69} - 12 q^{70} + 12 q^{72} - 20 q^{73} - 18 q^{76} + 8 q^{78} + 40 q^{79} + 16 q^{81} - 4 q^{82} - 60 q^{84} - 72 q^{87} - 12 q^{90} + 10 q^{91} + 104 q^{93} - 12 q^{94} - 178 q^{97}+O(q^{100}) \) 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9 + 20 * q^10 - 10 * q^13 - 20 * q^16 - 12 * q^18 - 12 * q^19 + 30 * q^21 + 10 * q^22 - 80 * q^25 + 18 * q^28 + 16 * q^31 + 72 * q^33 + 10 * q^34 + 8 * q^36 + 54 * q^39 - 20 * q^40 + 50 * q^43 + 8 * q^45 - 10 * q^46 + 8 * q^49 - 44 * q^51 - 10 * q^52 - 10 * q^55 + 30 * q^58 + 28 * q^63 + 20 * q^64 + 66 * q^66 + 60 * q^67 + 20 * q^69 - 12 * q^70 + 12 * q^72 - 20 * q^73 - 18 * q^76 + 8 * q^78 + 40 * q^79 + 16 * q^81 - 4 * q^82 - 60 * q^84 - 72 * q^87 - 12 * q^90 + 10 * q^91 + 104 * q^93 - 12 * q^94 - 178 * q^97

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